(x-4)(2x-2)=(x+4)(x-2)

Solution for (x-4)(2x-2)=(x+4)(x-2) equation:

Simplifying
(x + -4)(2x + -2) = (x + 4)(x + -2)

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

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

Multiply (-4 + x) * (-2 + 2x)
(-4(-2 + 2x) + x(-2 + 2x)) = (x + 4)(x + -2)
((-2 * -4 + 2x * -4) + x(-2 + 2x)) = (x + 4)(x + -2)
((8 + -8x) + x(-2 + 2x)) = (x + 4)(x + -2)
(8 + -8x + (-2 * x + 2x * x)) = (x + 4)(x + -2)
(8 + -8x + (-2x + 2x2)) = (x + 4)(x + -2)

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

Reorder the terms:
8 + -10x + 2x2 = (4 + x)(x + -2)

Reorder the terms:
8 + -10x + 2x2 = (4 + x)(-2 + x)

Multiply (4 + x) * (-2 + x)
8 + -10x + 2x2 = (4(-2 + x) + x(-2 + x))
8 + -10x + 2x2 = ((-2 * 4 + x * 4) + x(-2 + x))
8 + -10x + 2x2 = ((-8 + 4x) + x(-2 + x))
8 + -10x + 2x2 = (-8 + 4x + (-2 * x + x * x))
8 + -10x + 2x2 = (-8 + 4x + (-2x + x2))

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

Solving
8 + -10x + 2x2 = -8 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
8 + 8 + -10x + -2x + 2x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: 8 + 8 = 16
16 + -10x + -2x + 2x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: -10x + -2x = -12x
16 + -12x + 2x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
16 + -12x + 1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Reorder the terms:
16 + -12x + 1x2 = -8 + 8 + 2x + -2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
16 + -12x + 1x2 = 0 + 2x + -2x + x2 + -1x2
16 + -12x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
16 + -12x + 1x2 = 0 + x2 + -1x2
16 + -12x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -12x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -12x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12x + x2 = 0 + -16
-12x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-12x + x2 = -16

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -16 + 36

Reorder the terms:
36 + -12x + x2 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + -12x + x2 = 20

Factor a perfect square on the left side:
(x + -6)(x + -6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -6) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + -6 = 4.472135955

Simplifying
x + -6 = 4.472135955

Reorder the terms:
-6 + x = 4.472135955

Solving
-6 + x = 4.472135955

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4.472135955 + 6
x = 4.472135955 + 6

Combine like terms: 4.472135955 + 6 = 10.472135955
x = 10.472135955

Simplifying
x = 10.472135955

Subproblem 2
x + -6 = -4.472135955

Simplifying
x + -6 = -4.472135955

Reorder the terms:
-6 + x = -4.472135955

Solving
-6 + x = -4.472135955

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4.472135955 + 6
x = -4.472135955 + 6

Combine like terms: -4.472135955 + 6 = 1.527864045
x = 1.527864045

Simplifying
x = 1.527864045

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.472135955, 1.527864045}