2(4x-4)(4x-4)=108

Solution for 2(4x-4)(4x-4)=108 equation:

Simplifying
2(4x + -4)(4x + -4) = 108

Reorder the terms:
2(-4 + 4x)(4x + -4) = 108

Reorder the terms:
2(-4 + 4x)(-4 + 4x) = 108

Multiply (-4 + 4x) * (-4 + 4x)
2(-4(-4 + 4x) + 4x * (-4 + 4x)) = 108
2((-4 * -4 + 4x * -4) + 4x * (-4 + 4x)) = 108
2((16 + -16x) + 4x * (-4 + 4x)) = 108
2(16 + -16x + (-4 * 4x + 4x * 4x)) = 108
2(16 + -16x + (-16x + 16x2)) = 108

Combine like terms: -16x + -16x = -32x
2(16 + -32x + 16x2) = 108
(16 * 2 + -32x * 2 + 16x2 * 2) = 108
(32 + -64x + 32x2) = 108

Solving
32 + -64x + 32x2 = 108

Solving for variable 'x'.

Reorder the terms:
32 + -108 + -64x + 32x2 = 108 + -108

Combine like terms: 32 + -108 = -76
-76 + -64x + 32x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-76 + -64x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + -16x + 8x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-19 + -16x + 8x2)' equal to zero and attempt to solve:

Simplifying
-19 + -16x + 8x2 = 0

Solving
-19 + -16x + 8x2 = 0

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

Divide each side by '8'.
-2.375 + -2x + x2 = 0

Move the constant term to the right:

Add '2.375' to each side of the equation.
-2.375 + -2x + 2.375 + x2 = 0 + 2.375

Reorder the terms:
-2.375 + 2.375 + -2x + x2 = 0 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + -2x + x2 = 0 + 2.375
-2x + x2 = 0 + 2.375

Combine like terms: 0 + 2.375 = 2.375
-2x + x2 = 2.375

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 2.375 + 1

Reorder the terms:
1 + -2x + x2 = 2.375 + 1

Combine like terms: 2.375 + 1 = 3.375
1 + -2x + x2 = 3.375

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3.375

Calculate the square root of the right side: 1.837117307

Break this problem into two subproblems by setting 
(x + -1) equal to 1.837117307 and -1.837117307.

Subproblem 1
x + -1 = 1.837117307

Simplifying
x + -1 = 1.837117307

Reorder the terms:
-1 + x = 1.837117307

Solving
-1 + x = 1.837117307

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.837117307 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.837117307 + 1
x = 1.837117307 + 1

Combine like terms: 1.837117307 + 1 = 2.837117307
x = 2.837117307

Simplifying
x = 2.837117307

Subproblem 2
x + -1 = -1.837117307

Simplifying
x + -1 = -1.837117307

Reorder the terms:
-1 + x = -1.837117307

Solving
-1 + x = -1.837117307

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.837117307 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.837117307 + 1
x = -1.837117307 + 1

Combine like terms: -1.837117307 + 1 = -0.837117307
x = -0.837117307

Simplifying
x = -0.837117307

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.837117307, -0.837117307}
Solution
x = {2.837117307, -0.837117307}