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

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

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

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

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

Multiply (4 + x) * (4 + x)
((4(4 + x) + x(4 + x))) = ((x + -2)(2x + -2))
(((4 * 4 + x * 4) + x(4 + x))) = ((x + -2)(2x + -2))
(((16 + 4x) + x(4 + x))) = ((x + -2)(2x + -2))
((16 + 4x + (4 * x + x * x))) = ((x + -2)(2x + -2))
((16 + 4x + (4x + x2))) = ((x + -2)(2x + -2))

Combine like terms: 4x + 4x = 8x
((16 + 8x + x2)) = ((x + -2)(2x + -2))
(16 + 8x + x2) = ((x + -2)(2x + -2))

Remove parenthesis around (16 + 8x + x2)
16 + 8x + x2 = ((x + -2)(2x + -2))

Reorder the terms:
16 + 8x + x2 = ((-2 + x)(2x + -2))

Reorder the terms:
16 + 8x + x2 = ((-2 + x)(-2 + 2x))

Multiply (-2 + x) * (-2 + 2x)
16 + 8x + x2 = ((-2(-2 + 2x) + x(-2 + 2x)))
16 + 8x + x2 = (((-2 * -2 + 2x * -2) + x(-2 + 2x)))
16 + 8x + x2 = (((4 + -4x) + x(-2 + 2x)))
16 + 8x + x2 = ((4 + -4x + (-2 * x + 2x * x)))
16 + 8x + x2 = ((4 + -4x + (-2x + 2x2)))

Combine like terms: -4x + -2x = -6x
16 + 8x + x2 = ((4 + -6x + 2x2))
16 + 8x + x2 = (4 + -6x + 2x2)

Remove parenthesis around (4 + -6x + 2x2)
16 + 8x + x2 = 4 + -6x + 2x2

Solving
16 + 8x + x2 = 4 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
16 + -4 + 8x + 6x + x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Combine like terms: 16 + -4 = 12
12 + 8x + 6x + x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Combine like terms: 8x + 6x = 14x
12 + 14x + x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
12 + 14x + -1x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Reorder the terms:
12 + 14x + -1x2 = 4 + -4 + -6x + 6x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
12 + 14x + -1x2 = 0 + -6x + 6x + 2x2 + -2x2
12 + 14x + -1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
12 + 14x + -1x2 = 0 + 2x2 + -2x2
12 + 14x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + 14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + -14x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -14x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -14x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -14x + x2 = 0 + 12
-14x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-14x + x2 = 12

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 12 + 49

Reorder the terms:
49 + -14x + x2 = 12 + 49

Combine like terms: 12 + 49 = 61
49 + -14x + x2 = 61

Factor a perfect square on the left side:
(x + -7)(x + -7) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + -7) equal to 7.810249676 and -7.810249676.

Subproblem 1
x + -7 = 7.810249676

Simplifying
x + -7 = 7.810249676

Reorder the terms:
-7 + x = 7.810249676

Solving
-7 + x = 7.810249676

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 7.810249676 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.810249676 + 7
x = 7.810249676 + 7

Combine like terms: 7.810249676 + 7 = 14.810249676
x = 14.810249676

Simplifying
x = 14.810249676

Subproblem 2
x + -7 = -7.810249676

Simplifying
x + -7 = -7.810249676

Reorder the terms:
-7 + x = -7.810249676

Solving
-7 + x = -7.810249676

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -7.810249676 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.810249676 + 7
x = -7.810249676 + 7

Combine like terms: -7.810249676 + 7 = -0.810249676
x = -0.810249676

Simplifying
x = -0.810249676

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.810249676, -0.810249676}