(4x-4)(8x+4)=180

Solution for (4x-4)(8x+4)=180 equation:

Simplifying
(4x + -4)(8x + 4) = 180

Reorder the terms:
(-4 + 4x)(8x + 4) = 180

Reorder the terms:
(-4 + 4x)(4 + 8x) = 180

Multiply (-4 + 4x) * (4 + 8x)
(-4(4 + 8x) + 4x * (4 + 8x)) = 180
((4 * -4 + 8x * -4) + 4x * (4 + 8x)) = 180
((-16 + -32x) + 4x * (4 + 8x)) = 180
(-16 + -32x + (4 * 4x + 8x * 4x)) = 180
(-16 + -32x + (16x + 32x2)) = 180

Combine like terms: -32x + 16x = -16x
(-16 + -16x + 32x2) = 180

Solving
-16 + -16x + 32x2 = 180

Solving for variable 'x'.

Reorder the terms:
-16 + -180 + -16x + 32x2 = 180 + -180

Combine like terms: -16 + -180 = -196
-196 + -16x + 32x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-196 + -16x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-49 + -4x + 8x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-49 + -4x + 8x2)' equal to zero and attempt to solve:

Simplifying
-49 + -4x + 8x2 = 0

Solving
-49 + -4x + 8x2 = 0

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

Divide each side by '8'.
-6.125 + -0.5x + x2 = 0

Move the constant term to the right:

Add '6.125' to each side of the equation.
-6.125 + -0.5x + 6.125 + x2 = 0 + 6.125

Reorder the terms:
-6.125 + 6.125 + -0.5x + x2 = 0 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + -0.5x + x2 = 0 + 6.125
-0.5x + x2 = 0 + 6.125

Combine like terms: 0 + 6.125 = 6.125
-0.5x + x2 = 6.125

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 6.125 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6.125 + 0.0625

Combine like terms: 6.125 + 0.0625 = 6.1875
0.0625 + -0.5x + x2 = 6.1875

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.1875

Calculate the square root of the right side: 2.487468593

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.487468593 and -2.487468593.

Subproblem 1
x + -0.25 = 2.487468593

Simplifying
x + -0.25 = 2.487468593

Reorder the terms:
-0.25 + x = 2.487468593

Solving
-0.25 + x = 2.487468593

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 2.487468593 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.487468593 + 0.25
x = 2.487468593 + 0.25

Combine like terms: 2.487468593 + 0.25 = 2.737468593
x = 2.737468593

Simplifying
x = 2.737468593

Subproblem 2
x + -0.25 = -2.487468593

Simplifying
x + -0.25 = -2.487468593

Reorder the terms:
-0.25 + x = -2.487468593

Solving
-0.25 + x = -2.487468593

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -2.487468593 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.487468593 + 0.25
x = -2.487468593 + 0.25

Combine like terms: -2.487468593 + 0.25 = -2.237468593
x = -2.237468593

Simplifying
x = -2.237468593

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.737468593, -2.237468593}
Solution
x = {2.737468593, -2.237468593}