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

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


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

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

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

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

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

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

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

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

Combine like terms: -4x + -2x = -6x
-4 + 2x + 2x2 = (4 + -6x + 2x2)

Add '-2x2' to each side of the equation.
-4 + 2x + 2x2 + -2x2 = 4 + -6x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 2x + 0 = 4 + -6x + 2x2 + -2x2
-4 + 2x = 4 + -6x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 2x = 4 + -6x + 0
-4 + 2x = 4 + -6x

Solving
-4 + 2x = 4 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
-4 + 2x + 6x = 4 + -6x + 6x

Combine like terms: 2x + 6x = 8x
-4 + 8x = 4 + -6x + 6x

Combine like terms: -6x + 6x = 0
-4 + 8x = 4 + 0
-4 + 8x = 4

Add '4' to each side of the equation.
-4 + 4 + 8x = 4 + 4

Combine like terms: -4 + 4 = 0
0 + 8x = 4 + 4
8x = 4 + 4

Combine like terms: 4 + 4 = 8
8x = 8

Divide each side by '8'.
x = 1

Simplifying
x = 1

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