(a-b)(a+b)(b-c)(d+c)(c-a)(c+a)=0

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Solution for (a-b)(a+b)(b-c)(d+c)(c-a)(c+a)=0 equation:


Simplifying
(a + -1b)(a + b)(b + -1c)(d + c)(c + -1a)(c + a) = 0

Reorder the terms:
(a + -1b)(a + b)(b + -1c)(c + d)(c + -1a)(c + a) = 0

Reorder the terms:
(a + -1b)(a + b)(b + -1c)(c + d)(-1a + c)(c + a) = 0

Reorder the terms:
(a + -1b)(a + b)(b + -1c)(c + d)(-1a + c)(a + c) = 0

Multiply (a + -1b) * (a + b)
(a(a + b) + -1b * (a + b))(b + -1c)(c + d)(-1a + c)(a + c) = 0
((a * a + b * a) + -1b * (a + b))(b + -1c)(c + d)(-1a + c)(a + c) = 0

Reorder the terms:
((ab + a2) + -1b * (a + b))(b + -1c)(c + d)(-1a + c)(a + c) = 0
((ab + a2) + -1b * (a + b))(b + -1c)(c + d)(-1a + c)(a + c) = 0
(ab + a2 + (a * -1b + b * -1b))(b + -1c)(c + d)(-1a + c)(a + c) = 0
(ab + a2 + (-1ab + -1b2))(b + -1c)(c + d)(-1a + c)(a + c) = 0

Reorder the terms:
(ab + -1ab + a2 + -1b2)(b + -1c)(c + d)(-1a + c)(a + c) = 0

Combine like terms: ab + -1ab = 0
(0 + a2 + -1b2)(b + -1c)(c + d)(-1a + c)(a + c) = 0
(a2 + -1b2)(b + -1c)(c + d)(-1a + c)(a + c) = 0

Multiply (a2 + -1b2) * (b + -1c)
(a2(b + -1c) + -1b2 * (b + -1c))(c + d)(-1a + c)(a + c) = 0
((b * a2 + -1c * a2) + -1b2 * (b + -1c))(c + d)(-1a + c)(a + c) = 0
((a2b + -1a2c) + -1b2 * (b + -1c))(c + d)(-1a + c)(a + c) = 0
(a2b + -1a2c + (b * -1b2 + -1c * -1b2))(c + d)(-1a + c)(a + c) = 0

Reorder the terms:
(a2b + -1a2c + (1b2c + -1b3))(c + d)(-1a + c)(a + c) = 0
(a2b + -1a2c + (1b2c + -1b3))(c + d)(-1a + c)(a + c) = 0
(a2b + -1a2c + 1b2c + -1b3)(c + d)(-1a + c)(a + c) = 0

Multiply (a2b + -1a2c + 1b2c + -1b3) * (c + d)
(a2b(c + d) + -1a2c * (c + d) + 1b2c * (c + d) + -1b3 * (c + d))(-1a + c)(a + c) = 0
((c * a2b + d * a2b) + -1a2c * (c + d) + 1b2c * (c + d) + -1b3 * (c + d))(-1a + c)(a + c) = 0
((a2bc + a2bd) + -1a2c * (c + d) + 1b2c * (c + d) + -1b3 * (c + d))(-1a + c)(a + c) = 0
(a2bc + a2bd + (c * -1a2c + d * -1a2c) + 1b2c * (c + d) + -1b3 * (c + d))(-1a + c)(a + c) = 0

Reorder the terms:
(a2bc + a2bd + (-1a2cd + -1a2c2) + 1b2c * (c + d) + -1b3 * (c + d))(-1a + c)(a + c) = 0
(a2bc + a2bd + (-1a2cd + -1a2c2) + 1b2c * (c + d) + -1b3 * (c + d))(-1a + c)(a + c) = 0
(a2bc + a2bd + -1a2cd + -1a2c2 + (c * 1b2c + d * 1b2c) + -1b3 * (c + d))(-1a + c)(a + c) = 0

Reorder the terms:
(a2bc + a2bd + -1a2cd + -1a2c2 + (1b2cd + 1b2c2) + -1b3 * (c + d))(-1a + c)(a + c) = 0
(a2bc + a2bd + -1a2cd + -1a2c2 + (1b2cd + 1b2c2) + -1b3 * (c + d))(-1a + c)(a + c) = 0
(a2bc + a2bd + -1a2cd + -1a2c2 + 1b2cd + 1b2c2 + (c * -1b3 + d * -1b3))(-1a + c)(a + c) = 0
(a2bc + a2bd + -1a2cd + -1a2c2 + 1b2cd + 1b2c2 + (-1b3c + -1b3d))(-1a + c)(a + c) = 0
(a2bc + a2bd + -1a2cd + -1a2c2 + 1b2cd + 1b2c2 + -1b3c + -1b3d)(-1a + c)(a + c) = 0

Multiply (a2bc + a2bd + -1a2cd + -1a2c2 + 1b2cd + 1b2c2 + -1b3c + -1b3d) * (-1a + c)
(a2bc(-1a + c) + a2bd(-1a + c) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
((-1a * a2bc + c * a2bc) + a2bd(-1a + c) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0

Reorder the terms:
((a2bc2 + -1a3bc) + a2bd(-1a + c) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
((a2bc2 + -1a3bc) + a2bd(-1a + c) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + (-1a * a2bd + c * a2bd) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0

Reorder the terms:
(a2bc2 + -1a3bc + (a2bcd + -1a3bd) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + (a2bcd + -1a3bd) + -1a2cd * (-1a + c) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + (-1a * -1a2cd + c * -1a2cd) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0

Reorder the terms:
(a2bc2 + -1a3bc + a2bcd + -1a3bd + (-1a2c2d + 1a3cd) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + (-1a2c2d + 1a3cd) + -1a2c2 * (-1a + c) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + (-1a * -1a2c2 + c * -1a2c2) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0

Reorder the terms:
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + (-1a2c3 + 1a3c2) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + (-1a2c3 + 1a3c2) + 1b2cd * (-1a + c) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + (-1a * 1b2cd + c * 1b2cd) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + (-1ab2cd + 1b2c2d) + 1b2c2 * (-1a + c) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + -1ab2cd + 1b2c2d + (-1a * 1b2c2 + c * 1b2c2) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + -1ab2cd + 1b2c2d + (-1ab2c2 + 1b2c3) + -1b3c * (-1a + c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + -1ab2cd + 1b2c2d + -1ab2c2 + 1b2c3 + (-1a * -1b3c + c * -1b3c) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + -1ab2cd + 1b2c2d + -1ab2c2 + 1b2c3 + (1ab3c + -1b3c2) + -1b3d * (-1a + c))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + -1ab2cd + 1b2c2d + -1ab2c2 + 1b2c3 + 1ab3c + -1b3c2 + (-1a * -1b3d + c * -1b3d))(a + c) = 0
(a2bc2 + -1a3bc + a2bcd + -1a3bd + -1a2c2d + 1a3cd + -1a2c3 + 1a3c2 + -1ab2cd + 1b2c2d + -1ab2c2 + 1b2c3 + 1ab3c + -1b3c2 + (1ab3d + -1b3cd))(a + c) = 0

Reorder the terms:
(-1ab2cd + -1ab2c2 + 1ab3c + 1ab3d + a2bcd + a2bc2 + -1a2c2d + -1a2c3 + -1a3bc + -1a3bd + 1a3cd + 1a3c2 + 1b2c2d + 1b2c3 + -1b3cd + -1b3c2)(a + c) = 0
(-1ab2cd + -1ab2c2 + 1ab3c + 1ab3d + a2bcd + a2bc2 + -1a2c2d + -1a2c3 + -1a3bc + -1a3bd + 1a3cd + 1a3c2 + 1b2c2d + 1b2c3 + -1b3cd + -1b3c2)(a + c) = 0

Multiply (-1ab2cd + -1ab2c2 + 1ab3c + 1ab3d + a2bcd + a2bc2 + -1a2c2d + -1a2c3 + -1a3bc + -1a3bd + 1a3cd + 1a3c2 + 1b2c2d + 1b2c3 + -1b3cd + -1b3c2) * (a + c)
(-1ab2cd * (a + c) + -1ab2c2 * (a + c) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
((a * -1ab2cd + c * -1ab2cd) + -1ab2c2 * (a + c) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
((-1ab2c2d + -1a2b2cd) + -1ab2c2 * (a + c) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
((-1ab2c2d + -1a2b2cd) + -1ab2c2 * (a + c) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + (a * -1ab2c2 + c * -1ab2c2) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + (-1ab2c3 + -1a2b2c2) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + (-1ab2c3 + -1a2b2c2) + 1ab3c * (a + c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + (a * 1ab3c + c * 1ab3c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + (1ab3c2 + 1a2b3c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + (1ab3c2 + 1a2b3c) + 1ab3d * (a + c) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + (a * 1ab3d + c * 1ab3d) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + (1ab3cd + 1a2b3d) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + (1ab3cd + 1a2b3d) + a2bcd(a + c) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + (a * a2bcd + c * a2bcd) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + (a2bc2d + a3bcd) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + (a2bc2d + a3bcd) + a2bc2(a + c) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + (a * a2bc2 + c * a2bc2) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + (a2bc3 + a3bc2) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + (a2bc3 + a3bc2) + -1a2c2d * (a + c) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + (a * -1a2c2d + c * -1a2c2d) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + (-1a2c3d + -1a3c2d) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + (-1a2c3d + -1a3c2d) + -1a2c3 * (a + c) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + (a * -1a2c3 + c * -1a2c3) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + (-1a2c4 + -1a3c3) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + (-1a2c4 + -1a3c3) + -1a3bc * (a + c) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + (a * -1a3bc + c * -1a3bc) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + (-1a3bc2 + -1a4bc) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + (-1a3bc2 + -1a4bc) + -1a3bd * (a + c) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + (a * -1a3bd + c * -1a3bd) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + (-1a3bcd + -1a4bd) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + (-1a3bcd + -1a4bd) + 1a3cd * (a + c) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + (a * 1a3cd + c * 1a3cd) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + (1a3c2d + 1a4cd) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + (1a3c2d + 1a4cd) + 1a3c2 * (a + c) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + (a * 1a3c2 + c * 1a3c2) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0

Reorder the terms:
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + (1a3c3 + 1a4c2) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + (1a3c3 + 1a4c2) + 1b2c2d * (a + c) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + (a * 1b2c2d + c * 1b2c2d) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + (1ab2c2d + 1b2c3d) + 1b2c3 * (a + c) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + 1ab2c2d + 1b2c3d + (a * 1b2c3 + c * 1b2c3) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + 1ab2c2d + 1b2c3d + (1ab2c3 + 1b2c4) + -1b3cd * (a + c) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + 1ab2c2d + 1b2c3d + 1ab2c3 + 1b2c4 + (a * -1b3cd + c * -1b3cd) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + 1ab2c2d + 1b2c3d + 1ab2c3 + 1b2c4 + (-1ab3cd + -1b3c2d) + -1b3c2 * (a + c)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + 1ab2c2d + 1b2c3d + 1ab2c3 + 1b2c4 + -1ab3cd + -1b3c2d + (a * -1b3c2 + c * -1b3c2)) = 0
(-1ab2c2d + -1a2b2cd + -1ab2c3 + -1a2b2c2 + 1ab3c2 + 1a2b3c + 1ab3cd + 1a2b3d + a2bc2d + a3bcd + a2bc3 + a3bc2 + -1a2c3d + -1a3c2d + -1a2c4 + -1a3c3 + -1a3bc2 + -1a4bc + -1a3bcd + -1a4bd + 1a3c2d + 1a4cd + 1a3c3 + 1a4c2 + 1ab2c2d + 1b2c3d + 1ab2c3 + 1b2c4 + -1ab3cd + -1b3c2d + (-1ab3c2 + -1b3c3)) = 0

Reorder the terms:
(-1ab2c2d + 1ab2c2d + -1ab2c3 + 1ab2c3 + 1ab3cd + -1ab3cd + 1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: -1ab2c2d + 1ab2c2d = 0
(0 + -1ab2c3 + 1ab2c3 + 1ab3cd + -1ab3cd + 1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(-1ab2c3 + 1ab2c3 + 1ab3cd + -1ab3cd + 1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: -1ab2c3 + 1ab2c3 = 0
(0 + 1ab3cd + -1ab3cd + 1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(1ab3cd + -1ab3cd + 1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: 1ab3cd + -1ab3cd = 0
(0 + 1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(1ab3c2 + -1ab3c2 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: 1ab3c2 + -1ab3c2 = 0
(0 + a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bcd + -1a3bcd + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: a3bcd + -1a3bcd = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + 0 + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + a3bc2 + -1a3bc2 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: a3bc2 + -1a3bc2 = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + 0 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + -1a3c2d + 1a3c2d + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: -1a3c2d + 1a3c2d = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + 0 + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + -1a3c3 + 1a3c3 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Combine like terms: -1a3c3 + 1a3c3 = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + 0 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0
(a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3) = 0

Solving
a2bc2d + a2bc3 + -1a2b2cd + -1a2b2c2 + 1a2b3c + 1a2b3d + -1a2c3d + -1a2c4 + -1a4bc + -1a4bd + 1a4cd + 1a4c2 + 1b2c3d + 1b2c4 + -1b3c2d + -1b3c3 = 0

Solving for variable 'a'.

The solution to this equation could not be determined.

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