=(a+b+c)(a+b+c)(a+b+c)(a+b+c)

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Solution for =(a+b+c)(a+b+c)(a+b+c)(a+b+c) equation:


Simplifying
0 = (a + b + c)(a + b + c)(a + b + c)(a + b + c)

Multiply (a + b + c) * (a + b + c)
0 = (a(a + b + c) + b(a + b + c) + c(a + b + c))(a + b + c)(a + b + c)
0 = ((a * a + b * a + c * a) + b(a + b + c) + c(a + b + c))(a + b + c)(a + b + c)

Reorder the terms:
0 = ((ab + ac + a2) + b(a + b + c) + c(a + b + c))(a + b + c)(a + b + c)
0 = ((ab + ac + a2) + b(a + b + c) + c(a + b + c))(a + b + c)(a + b + c)
0 = (ab + ac + a2 + (a * b + b * b + c * b) + c(a + b + c))(a + b + c)(a + b + c)

Reorder the terms:
0 = (ab + ac + a2 + (ab + bc + b2) + c(a + b + c))(a + b + c)(a + b + c)
0 = (ab + ac + a2 + (ab + bc + b2) + c(a + b + c))(a + b + c)(a + b + c)
0 = (ab + ac + a2 + ab + bc + b2 + (a * c + b * c + c * c))(a + b + c)(a + b + c)
0 = (ab + ac + a2 + ab + bc + b2 + (ac + bc + c2))(a + b + c)(a + b + c)

Reorder the terms:
0 = (ab + ab + ac + ac + a2 + bc + bc + b2 + c2)(a + b + c)(a + b + c)

Combine like terms: ab + ab = 2ab
0 = (2ab + ac + ac + a2 + bc + bc + b2 + c2)(a + b + c)(a + b + c)

Combine like terms: ac + ac = 2ac
0 = (2ab + 2ac + a2 + bc + bc + b2 + c2)(a + b + c)(a + b + c)

Combine like terms: bc + bc = 2bc
0 = (2ab + 2ac + a2 + 2bc + b2 + c2)(a + b + c)(a + b + c)

Multiply (2ab + 2ac + a2 + 2bc + b2 + c2) * (a + b + c)
0 = (2ab * (a + b + c) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = ((a * 2ab + b * 2ab + c * 2ab) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)

Reorder the terms:
0 = ((2abc + 2ab2 + 2a2b) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = ((2abc + 2ab2 + 2a2b) + 2ac * (a + b + c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + (a * 2ac + b * 2ac + c * 2ac) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + (2abc + 2ac2 + 2a2c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + (2abc + 2ac2 + 2a2c) + a2(a + b + c) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + (a * a2 + b * a2 + c * a2) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + (a2b + a2c + a3) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + (a2b + a2c + a3) + 2bc * (a + b + c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + (a * 2bc + b * 2bc + c * 2bc) + b2(a + b + c) + c2(a + b + c))(a + b + c)

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + (2abc + 2bc2 + 2b2c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + (2abc + 2bc2 + 2b2c) + b2(a + b + c) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + (a * b2 + b * b2 + c * b2) + c2(a + b + c))(a + b + c)

Reorder the terms:
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + (ab2 + b2c + b3) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + (ab2 + b2c + b3) + c2(a + b + c))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + ab2 + b2c + b3 + (a * c2 + b * c2 + c * c2))(a + b + c)
0 = (2abc + 2ab2 + 2a2b + 2abc + 2ac2 + 2a2c + a2b + a2c + a3 + 2abc + 2bc2 + 2b2c + ab2 + b2c + b3 + (ac2 + bc2 + c3))(a + b + c)

Reorder the terms:
0 = (2abc + 2abc + 2abc + 2ab2 + ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2abc + 2abc = 4abc
0 = (4abc + 2abc + 2ab2 + ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 4abc + 2abc = 6abc
0 = (6abc + 2ab2 + ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2ab2 + ab2 = 3ab2
0 = (6abc + 3ab2 + 2ac2 + ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2ac2 + ac2 = 3ac2
0 = (6abc + 3ab2 + 3ac2 + 2a2b + a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2a2b + a2b = 3a2b
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 2a2c + a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2a2c + a2c = 3a2c
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 2bc2 + bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2bc2 + bc2 = 3bc2
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 2b2c + b2c + b3 + c3)(a + b + c)

Combine like terms: 2b2c + b2c = 3b2c
0 = (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3)(a + b + c)

Multiply (6abc + 3ab2 + 3ac2 + 3a2b + 3a2c + a3 + 3bc2 + 3b2c + b3 + c3) * (a + b + c)
0 = (6abc * (a + b + c) + 3ab2 * (a + b + c) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = ((a * 6abc + b * 6abc + c * 6abc) + 3ab2 * (a + b + c) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = ((6abc2 + 6ab2c + 6a2bc) + 3ab2 * (a + b + c) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = ((6abc2 + 6ab2c + 6a2bc) + 3ab2 * (a + b + c) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + (a * 3ab2 + b * 3ab2 + c * 3ab2) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + (3ab2c + 3ab3 + 3a2b2) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + (3ab2c + 3ab3 + 3a2b2) + 3ac2 * (a + b + c) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + (a * 3ac2 + b * 3ac2 + c * 3ac2) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + (3abc2 + 3ac3 + 3a2c2) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + (3abc2 + 3ac3 + 3a2c2) + 3a2b * (a + b + c) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + (a * 3a2b + b * 3a2b + c * 3a2b) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + (3a2bc + 3a2b2 + 3a3b) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + (3a2bc + 3a2b2 + 3a3b) + 3a2c * (a + b + c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + (a * 3a2c + b * 3a2c + c * 3a2c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + (3a2bc + 3a2c2 + 3a3c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + (3a2bc + 3a2c2 + 3a3c) + a3(a + b + c) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + (a * a3 + b * a3 + c * a3) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + (a3b + a3c + a4) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + (a3b + a3c + a4) + 3bc2 * (a + b + c) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + (a * 3bc2 + b * 3bc2 + c * 3bc2) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + (3abc2 + 3bc3 + 3b2c2) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + (3abc2 + 3bc3 + 3b2c2) + 3b2c * (a + b + c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + (a * 3b2c + b * 3b2c + c * 3b2c) + b3(a + b + c) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + (3ab2c + 3b2c2 + 3b3c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + (3ab2c + 3b2c2 + 3b3c) + b3(a + b + c) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + 3ab2c + 3b2c2 + 3b3c + (a * b3 + b * b3 + c * b3) + c3(a + b + c))

Reorder the terms:
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + 3ab2c + 3b2c2 + 3b3c + (ab3 + b3c + b4) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + 3ab2c + 3b2c2 + 3b3c + (ab3 + b3c + b4) + c3(a + b + c))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + 3ab2c + 3b2c2 + 3b3c + ab3 + b3c + b4 + (a * c3 + b * c3 + c * c3))
0 = (6abc2 + 6ab2c + 6a2bc + 3ab2c + 3ab3 + 3a2b2 + 3abc2 + 3ac3 + 3a2c2 + 3a2bc + 3a2b2 + 3a3b + 3a2bc + 3a2c2 + 3a3c + a3b + a3c + a4 + 3abc2 + 3bc3 + 3b2c2 + 3ab2c + 3b2c2 + 3b3c + ab3 + b3c + b4 + (ac3 + bc3 + c4))

Reorder the terms:
0 = (6abc2 + 3abc2 + 3abc2 + 6ab2c + 3ab2c + 3ab2c + 3ab3 + ab3 + 3ac3 + ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 6abc2 + 3abc2 = 9abc2
0 = (9abc2 + 3abc2 + 6ab2c + 3ab2c + 3ab2c + 3ab3 + ab3 + 3ac3 + ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 9abc2 + 3abc2 = 12abc2
0 = (12abc2 + 6ab2c + 3ab2c + 3ab2c + 3ab3 + ab3 + 3ac3 + ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 6ab2c + 3ab2c = 9ab2c
0 = (12abc2 + 9ab2c + 3ab2c + 3ab3 + ab3 + 3ac3 + ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 9ab2c + 3ab2c = 12ab2c
0 = (12abc2 + 12ab2c + 3ab3 + ab3 + 3ac3 + ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3ab3 + ab3 = 4ab3
0 = (12abc2 + 12ab2c + 4ab3 + 3ac3 + ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3ac3 + ac3 = 4ac3
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 6a2bc + 3a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 6a2bc + 3a2bc = 9a2bc
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 9a2bc + 3a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 9a2bc + 3a2bc = 12a2bc
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 3a2b2 + 3a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3a2b2 + 3a2b2 = 6a2b2
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 3a2c2 + 3a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3a2c2 + 3a2c2 = 6a2c2
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 3a3b + a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3a3b + a3b = 4a3b
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 3a3c + a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3a3c + a3c = 4a3c
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 3bc3 + bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3bc3 + bc3 = 4bc3
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 3b2c2 + 3b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3b2c2 + 3b2c2 = 6b2c2
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 3b3c + b3c + b4 + c4)

Combine like terms: 3b3c + b3c = 4b3c
0 = (12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4)

Solving
0 = 12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4

Solving for variable 'a'.
Remove the zero:
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4 + -12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4

Reorder the terms:
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 12abc2 + -12abc2 + 12ab2c + -12ab2c + 4ab3 + -4ab3 + 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 12abc2 + -12abc2 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 12ab2c + -12ab2c + 4ab3 + -4ab3 + 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 12ab2c + -12ab2c + 4ab3 + -4ab3 + 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 12ab2c + -12ab2c = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 4ab3 + -4ab3 + 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 4ab3 + -4ab3 + 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 4ab3 + -4ab3 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 4ac3 + -4ac3 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 4ac3 + -4ac3 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 12a2bc + -12a2bc + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 12a2bc + -12a2bc = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 6a2b2 + -6a2b2 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 6a2b2 + -6a2b2 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 6a2c2 + -6a2c2 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 6a2c2 + -6a2c2 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 4a3b + -4a3b + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 4a3b + -4a3b = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 4a3c + -4a3c + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 4a3c + -4a3c = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = a4 + -1a4 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: a4 + -1a4 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 4bc3 + -4bc3 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 4bc3 + -4bc3 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 6b2c2 + -6b2c2 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 6b2c2 + -6b2c2 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 4b3c + -4b3c + b4 + -1b4 + c4 + -1c4

Combine like terms: 4b3c + -4b3c = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + b4 + -1b4 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = b4 + -1b4 + c4 + -1c4

Combine like terms: b4 + -1b4 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0 + c4 + -1c4
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = c4 + -1c4

Combine like terms: c4 + -1c4 = 0
-12abc2 + -12ab2c + -4ab3 + -4ac3 + -12a2bc + -6a2b2 + -6a2c2 + -4a3b + -4a3c + -1a4 + -4bc3 + -6b2c2 + -4b3c + -1b4 + -1c4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4)' equal to zero and attempt to solve: Simplifying 12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4 = 0 Solving 12abc2 + 12ab2c + 4ab3 + 4ac3 + 12a2bc + 6a2b2 + 6a2c2 + 4a3b + 4a3c + a4 + 4bc3 + 6b2c2 + 4b3c + b4 + c4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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