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

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


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

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

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

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

Combine like terms: -2x + 4x = 2x
(-4 + 2x + 2x2) = (x + -2)(x + -1)

Reorder the terms:
-4 + 2x + 2x2 = (-2 + x)(x + -1)

Reorder the terms:
-4 + 2x + 2x2 = (-2 + x)(-1 + x)

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

Combine like terms: -2x + -1x = -3x
-4 + 2x + 2x2 = (2 + -3x + x2)

Solving
-4 + 2x + 2x2 = 2 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -2 + 2x + 3x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: -4 + -2 = -6
-6 + 2x + 3x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: 2x + 3x = 5x
-6 + 5x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-6 + 5x + 1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Reorder the terms:
-6 + 5x + 1x2 = 2 + -2 + -3x + 3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-6 + 5x + 1x2 = 0 + -3x + 3x + x2 + -1x2
-6 + 5x + 1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-6 + 5x + 1x2 = 0 + x2 + -1x2
-6 + 5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 5x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 1}

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