(2x-2)(5x+2)=(2x-2)(x-2)

Solution for (2x-2)(5x+2)=(2x-2)(x-2) equation:

Simplifying
(2x + -2)(5x + 2) = (2x + -2)(x + -2)

Reorder the terms:
(-2 + 2x)(5x + 2) = (2x + -2)(x + -2)

Reorder the terms:
(-2 + 2x)(2 + 5x) = (2x + -2)(x + -2)

Multiply (-2 + 2x) * (2 + 5x)
(-2(2 + 5x) + 2x * (2 + 5x)) = (2x + -2)(x + -2)
((2 * -2 + 5x * -2) + 2x * (2 + 5x)) = (2x + -2)(x + -2)
((-4 + -10x) + 2x * (2 + 5x)) = (2x + -2)(x + -2)
(-4 + -10x + (2 * 2x + 5x * 2x)) = (2x + -2)(x + -2)
(-4 + -10x + (4x + 10x2)) = (2x + -2)(x + -2)

Combine like terms: -10x + 4x = -6x
(-4 + -6x + 10x2) = (2x + -2)(x + -2)

Reorder the terms:
-4 + -6x + 10x2 = (-2 + 2x)(x + -2)

Reorder the terms:
-4 + -6x + 10x2 = (-2 + 2x)(-2 + x)

Multiply (-2 + 2x) * (-2 + x)
-4 + -6x + 10x2 = (-2(-2 + x) + 2x * (-2 + x))
-4 + -6x + 10x2 = ((-2 * -2 + x * -2) + 2x * (-2 + x))
-4 + -6x + 10x2 = ((4 + -2x) + 2x * (-2 + x))
-4 + -6x + 10x2 = (4 + -2x + (-2 * 2x + x * 2x))
-4 + -6x + 10x2 = (4 + -2x + (-4x + 2x2))

Combine like terms: -2x + -4x = -6x
-4 + -6x + 10x2 = (4 + -6x + 2x2)

Add '6x' to each side of the equation.
-4 + -6x + 6x + 10x2 = 4 + -6x + 6x + 2x2

Combine like terms: -6x + 6x = 0
-4 + 0 + 10x2 = 4 + -6x + 6x + 2x2
-4 + 10x2 = 4 + -6x + 6x + 2x2

Combine like terms: -6x + 6x = 0
-4 + 10x2 = 4 + 0 + 2x2
-4 + 10x2 = 4 + 2x2

Solving
-4 + 10x2 = 4 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
-4 + 10x2 + -2x2 = 4 + 2x2 + -2x2

Combine like terms: 10x2 + -2x2 = 8x2
-4 + 8x2 = 4 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 8x2 = 4 + 0
-4 + 8x2 = 4

Add '4' to each side of the equation.
-4 + 4 + 8x2 = 4 + 4

Combine like terms: -4 + 4 = 0
0 + 8x2 = 4 + 4
8x2 = 4 + 4

Combine like terms: 4 + 4 = 8
8x2 = 8

Divide each side by '8'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}