2[(4x-2)(4x-2)]=120

Solution for 2[(4x-2)(4x-2)]=120 equation:

Simplifying
2[(4x + -2)(4x + -2)] = 120

Reorder the terms:
2[(-2 + 4x)(4x + -2)] = 120

Reorder the terms:
2[(-2 + 4x)(-2 + 4x)] = 120

Multiply (-2 + 4x) * (-2 + 4x)
2[(-2(-2 + 4x) + 4x * (-2 + 4x))] = 120
2[((-2 * -2 + 4x * -2) + 4x * (-2 + 4x))] = 120
2[((4 + -8x) + 4x * (-2 + 4x))] = 120
2[(4 + -8x + (-2 * 4x + 4x * 4x))] = 120
2[(4 + -8x + (-8x + 16x2))] = 120

Combine like terms: -8x + -8x = -16x
2[(4 + -16x + 16x2)] = 120
[4 * 2 + -16x * 2 + 16x2 * 2] = 120
[8 + -32x + 32x2] = 120

Solving
8 + -32x + 32x2 = 120

Solving for variable 'x'.

Reorder the terms:
8 + -120 + -32x + 32x2 = 120 + -120

Combine like terms: 8 + -120 = -112
-112 + -32x + 32x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-112 + -32x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-7 + -2x + 2x2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-7 + -2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-7 + -2x + 2x2 = 0

Solving
-7 + -2x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -1x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -1x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -1x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -1x + x2 = 0 + 3.5
-1x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-1x + x2 = 3.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 3.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
0.25 + -1x + x2 = 3.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
x + -0.5 = 1.936491673

Simplifying
x + -0.5 = 1.936491673

Reorder the terms:
-0.5 + x = 1.936491673

Solving
-0.5 + x = 1.936491673

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.936491673 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.936491673 + 0.5
x = 1.936491673 + 0.5

Combine like terms: 1.936491673 + 0.5 = 2.436491673
x = 2.436491673

Simplifying
x = 2.436491673

Subproblem 2
x + -0.5 = -1.936491673

Simplifying
x + -0.5 = -1.936491673

Reorder the terms:
-0.5 + x = -1.936491673

Solving
-0.5 + x = -1.936491673

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.936491673 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.936491673 + 0.5
x = -1.936491673 + 0.5

Combine like terms: -1.936491673 + 0.5 = -1.436491673
x = -1.436491673

Simplifying
x = -1.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.436491673, -1.436491673}
Solution
x = {2.436491673, -1.436491673}