(r^2-1)(r+1)+2(r-1)(r^2-1)=(r-2)(r-1)(r+1)

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Solution for (r^2-1)(r+1)+2(r-1)(r^2-1)=(r-2)(r-1)(r+1) equation: 


Simplifying
(r2 + -1)(r + 1) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)

Reorder the terms:
(-1 + r2)(r + 1) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)

Reorder the terms:
(-1 + r2)(1 + r) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)

Multiply (-1 + r2) * (1 + r)
(-1(1 + r) + r2(1 + r)) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)
((1 * -1 + r * -1) + r2(1 + r)) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)
((-1 + -1r) + r2(1 + r)) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)
(-1 + -1r + (1 * r2 + r * r2)) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)
(-1 + -1r + (1r2 + r3)) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)
(-1 + -1r + 1r2 + r3) + 2(r + -1)(r2 + -1) = (r + -2)(r + -1)(r + 1)

Reorder the terms:
-1 + -1r + 1r2 + r3 + 2(-1 + r)(r2 + -1) = (r + -2)(r + -1)(r + 1)

Reorder the terms:
-1 + -1r + 1r2 + r3 + 2(-1 + r)(-1 + r2) = (r + -2)(r + -1)(r + 1)

Multiply (-1 + r) * (-1 + r2)
-1 + -1r + 1r2 + r3 + 2(-1(-1 + r2) + r(-1 + r2)) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + 2((-1 * -1 + r2 * -1) + r(-1 + r2)) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + 2((1 + -1r2) + r(-1 + r2)) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + 2(1 + -1r2 + (-1 * r + r2 * r)) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + 2(1 + -1r2 + (-1r + r3)) = (r + -2)(r + -1)(r + 1)

Reorder the terms:
-1 + -1r + 1r2 + r3 + 2(1 + -1r + -1r2 + r3) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + 2(1 + -1r + -1r2 + r3) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + (1 * 2 + -1r * 2 + -1r2 * 2 + r3 * 2) = (r + -2)(r + -1)(r + 1)
-1 + -1r + 1r2 + r3 + (2 + -2r + -2r2 + 2r3) = (r + -2)(r + -1)(r + 1)

Reorder the terms:
-1 + 2 + -1r + -2r + 1r2 + -2r2 + r3 + 2r3 = (r + -2)(r + -1)(r + 1)

Combine like terms: -1 + 2 = 1
1 + -1r + -2r + 1r2 + -2r2 + r3 + 2r3 = (r + -2)(r + -1)(r + 1)

Combine like terms: -1r + -2r = -3r
1 + -3r + 1r2 + -2r2 + r3 + 2r3 = (r + -2)(r + -1)(r + 1)

Combine like terms: 1r2 + -2r2 = -1r2
1 + -3r + -1r2 + r3 + 2r3 = (r + -2)(r + -1)(r + 1)

Combine like terms: r3 + 2r3 = 3r3
1 + -3r + -1r2 + 3r3 = (r + -2)(r + -1)(r + 1)

Reorder the terms:
1 + -3r + -1r2 + 3r3 = (-2 + r)(r + -1)(r + 1)

Reorder the terms:
1 + -3r + -1r2 + 3r3 = (-2 + r)(-1 + r)(r + 1)

Reorder the terms:
1 + -3r + -1r2 + 3r3 = (-2 + r)(-1 + r)(1 + r)

Multiply (-2 + r) * (-1 + r)
1 + -3r + -1r2 + 3r3 = (-2(-1 + r) + r(-1 + r))(1 + r)
1 + -3r + -1r2 + 3r3 = ((-1 * -2 + r * -2) + r(-1 + r))(1 + r)
1 + -3r + -1r2 + 3r3 = ((2 + -2r) + r(-1 + r))(1 + r)
1 + -3r + -1r2 + 3r3 = (2 + -2r + (-1 * r + r * r))(1 + r)
1 + -3r + -1r2 + 3r3 = (2 + -2r + (-1r + r2))(1 + r)

Combine like terms: -2r + -1r = -3r
1 + -3r + -1r2 + 3r3 = (2 + -3r + r2)(1 + r)

Multiply (2 + -3r + r2) * (1 + r)
1 + -3r + -1r2 + 3r3 = (2(1 + r) + -3r * (1 + r) + r2(1 + r))
1 + -3r + -1r2 + 3r3 = ((1 * 2 + r * 2) + -3r * (1 + r) + r2(1 + r))
1 + -3r + -1r2 + 3r3 = ((2 + 2r) + -3r * (1 + r) + r2(1 + r))
1 + -3r + -1r2 + 3r3 = (2 + 2r + (1 * -3r + r * -3r) + r2(1 + r))
1 + -3r + -1r2 + 3r3 = (2 + 2r + (-3r + -3r2) + r2(1 + r))
1 + -3r + -1r2 + 3r3 = (2 + 2r + -3r + -3r2 + (1 * r2 + r * r2))
1 + -3r + -1r2 + 3r3 = (2 + 2r + -3r + -3r2 + (1r2 + r3))

Combine like terms: 2r + -3r = -1r
1 + -3r + -1r2 + 3r3 = (2 + -1r + -3r2 + 1r2 + r3)

Combine like terms: -3r2 + 1r2 = -2r2
1 + -3r + -1r2 + 3r3 = (2 + -1r + -2r2 + r3)

Solving
1 + -3r + -1r2 + 3r3 = 2 + -1r + -2r2 + r3

Solving for variable 'r'.

Reorder the terms:
1 + -2 + -3r + r + -1r2 + 2r2 + 3r3 + -1r3 = 2 + -1r + -2r2 + r3 + -2 + r + 2r2 + -1r3

Combine like terms: 1 + -2 = -1
-1 + -3r + r + -1r2 + 2r2 + 3r3 + -1r3 = 2 + -1r + -2r2 + r3 + -2 + r + 2r2 + -1r3

Combine like terms: -3r + r = -2r
-1 + -2r + -1r2 + 2r2 + 3r3 + -1r3 = 2 + -1r + -2r2 + r3 + -2 + r + 2r2 + -1r3

Combine like terms: -1r2 + 2r2 = 1r2
-1 + -2r + 1r2 + 3r3 + -1r3 = 2 + -1r + -2r2 + r3 + -2 + r + 2r2 + -1r3

Combine like terms: 3r3 + -1r3 = 2r3
-1 + -2r + 1r2 + 2r3 = 2 + -1r + -2r2 + r3 + -2 + r + 2r2 + -1r3

Reorder the terms:
-1 + -2r + 1r2 + 2r3 = 2 + -2 + -1r + r + -2r2 + 2r2 + r3 + -1r3

Combine like terms: 2 + -2 = 0
-1 + -2r + 1r2 + 2r3 = 0 + -1r + r + -2r2 + 2r2 + r3 + -1r3
-1 + -2r + 1r2 + 2r3 = -1r + r + -2r2 + 2r2 + r3 + -1r3

Combine like terms: -1r + r = 0
-1 + -2r + 1r2 + 2r3 = 0 + -2r2 + 2r2 + r3 + -1r3
-1 + -2r + 1r2 + 2r3 = -2r2 + 2r2 + r3 + -1r3

Combine like terms: -2r2 + 2r2 = 0
-1 + -2r + 1r2 + 2r3 = 0 + r3 + -1r3
-1 + -2r + 1r2 + 2r3 = r3 + -1r3

Combine like terms: r3 + -1r3 = 0
-1 + -2r + 1r2 + 2r3 = 0

The solution to this equation could not be determined.

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