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

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


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

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

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

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

Combine like terms: -1x + 1x = 0
2(-1 + 0 + x2) = x2 + -1x
2(-1 + x2) = x2 + -1x
(-1 * 2 + x2 * 2) = x2 + -1x
(-2 + 2x2) = x2 + -1x

Reorder the terms:
-2 + 2x2 = -1x + x2

Solving
-2 + 2x2 = -1x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + x + 2x2 + -1x2 = -1x + x2 + x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-2 + x + 1x2 = -1x + x2 + x + -1x2

Reorder the terms:
-2 + x + 1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-2 + x + 1x2 = 0 + x2 + -1x2
-2 + x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + x + 1x2 = 0

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


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1}

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