(x^2-1)*(2*x-2)-(x^2-2*x+1)*(2*x)=0

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Solution for (x^2-1)*(2*x-2)-(x^2-2*x+1)*(2*x)=0 equation: 


Simplifying
(x2 + -1)(2x + -2) + -1(x2 + -2x + 1)(2x) = 0

Reorder the terms:
(-1 + x2)(2x + -2) + -1(x2 + -2x + 1)(2x) = 0

Reorder the terms:
(-1 + x2)(-2 + 2x) + -1(x2 + -2x + 1)(2x) = 0

Multiply (-1 + x2) * (-2 + 2x)
(-1(-2 + 2x) + x2(-2 + 2x)) + -1(x2 + -2x + 1)(2x) = 0
((-2 * -1 + 2x * -1) + x2(-2 + 2x)) + -1(x2 + -2x + 1)(2x) = 0
((2 + -2x) + x2(-2 + 2x)) + -1(x2 + -2x + 1)(2x) = 0
(2 + -2x + (-2 * x2 + 2x * x2)) + -1(x2 + -2x + 1)(2x) = 0
(2 + -2x + (-2x2 + 2x3)) + -1(x2 + -2x + 1)(2x) = 0
(2 + -2x + -2x2 + 2x3) + -1(x2 + -2x + 1)(2x) = 0

Reorder the terms:
2 + -2x + -2x2 + 2x3 + -1(1 + -2x + x2)(2x) = 0

Remove parenthesis around (2x)
2 + -2x + -2x2 + 2x3 + -1(1 + -2x + x2) * 2x = 0

Reorder the terms for easier multiplication:
2 + -2x + -2x2 + 2x3 + -1 * 2x(1 + -2x + x2) = 0

Multiply -1 * 2
2 + -2x + -2x2 + 2x3 + -2x(1 + -2x + x2) = 0
2 + -2x + -2x2 + 2x3 + (1 * -2x + -2x * -2x + x2 * -2x) = 0
2 + -2x + -2x2 + 2x3 + (-2x + 4x2 + -2x3) = 0

Reorder the terms:
2 + -2x + -2x + -2x2 + 4x2 + 2x3 + -2x3 = 0

Combine like terms: -2x + -2x = -4x
2 + -4x + -2x2 + 4x2 + 2x3 + -2x3 = 0

Combine like terms: -2x2 + 4x2 = 2x2
2 + -4x + 2x2 + 2x3 + -2x3 = 0

Combine like terms: 2x3 + -2x3 = 0
2 + -4x + 2x2 + 0 = 0
2 + -4x + 2x2 = 0

Solving
2 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2x + x2) = 0

Factor a trinomial.
2((1 + -1x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {1, 1}

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