(8x-8)(7x+8)=180

Solution for (8x-8)(7x+8)=180 equation:

Simplifying
(8x + -8)(7x + 8) = 180

Reorder the terms:
(-8 + 8x)(7x + 8) = 180

Reorder the terms:
(-8 + 8x)(8 + 7x) = 180

Multiply (-8 + 8x) * (8 + 7x)
(-8(8 + 7x) + 8x * (8 + 7x)) = 180
((8 * -8 + 7x * -8) + 8x * (8 + 7x)) = 180
((-64 + -56x) + 8x * (8 + 7x)) = 180
(-64 + -56x + (8 * 8x + 7x * 8x)) = 180
(-64 + -56x + (64x + 56x2)) = 180

Combine like terms: -56x + 64x = 8x
(-64 + 8x + 56x2) = 180

Solving
-64 + 8x + 56x2 = 180

Solving for variable 'x'.

Reorder the terms:
-64 + -180 + 8x + 56x2 = 180 + -180

Combine like terms: -64 + -180 = -244
-244 + 8x + 56x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-244 + 8x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-61 + 2x + 14x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-61 + 2x + 14x2)' equal to zero and attempt to solve:

Simplifying
-61 + 2x + 14x2 = 0

Solving
-61 + 2x + 14x2 = 0

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

Divide each side by '14'.
-4.357142857 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '4.357142857' to each side of the equation.
-4.357142857 + 0.1428571429x + 4.357142857 + x2 = 0 + 4.357142857

Reorder the terms:
-4.357142857 + 4.357142857 + 0.1428571429x + x2 = 0 + 4.357142857

Combine like terms: -4.357142857 + 4.357142857 = 0.000000000
0.000000000 + 0.1428571429x + x2 = 0 + 4.357142857
0.1428571429x + x2 = 0 + 4.357142857

Combine like terms: 0 + 4.357142857 = 4.357142857
0.1428571429x + x2 = 4.357142857

The x term is 0.1428571429x.  Take half its coefficient (0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
0.1428571429x + 0.005102040819 + x2 = 4.357142857 + 0.005102040819

Reorder the terms:
0.005102040819 + 0.1428571429x + x2 = 4.357142857 + 0.005102040819

Combine like terms: 4.357142857 + 0.005102040819 = 4.362244897819
0.005102040819 + 0.1428571429x + x2 = 4.362244897819

Factor a perfect square on the left side:
(x + 0.07142857145)(x + 0.07142857145) = 4.362244897819

Calculate the square root of the right side: 2.088598788

Break this problem into two subproblems by setting 
(x + 0.07142857145) equal to 2.088598788 and -2.088598788.

Subproblem 1
x + 0.07142857145 = 2.088598788

Simplifying
x + 0.07142857145 = 2.088598788

Reorder the terms:
0.07142857145 + x = 2.088598788

Solving
0.07142857145 + x = 2.088598788

Solving for variable 'x'.

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

Add '-0.07142857145' to each side of the equation.
0.07142857145 + -0.07142857145 + x = 2.088598788 + -0.07142857145

Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000
0.00000000000 + x = 2.088598788 + -0.07142857145
x = 2.088598788 + -0.07142857145

Combine like terms: 2.088598788 + -0.07142857145 = 2.01717021655
x = 2.01717021655

Simplifying
x = 2.01717021655

Subproblem 2
x + 0.07142857145 = -2.088598788

Simplifying
x + 0.07142857145 = -2.088598788

Reorder the terms:
0.07142857145 + x = -2.088598788

Solving
0.07142857145 + x = -2.088598788

Solving for variable 'x'.

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

Add '-0.07142857145' to each side of the equation.
0.07142857145 + -0.07142857145 + x = -2.088598788 + -0.07142857145

Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000
0.00000000000 + x = -2.088598788 + -0.07142857145
x = -2.088598788 + -0.07142857145

Combine like terms: -2.088598788 + -0.07142857145 = -2.16002735945
x = -2.16002735945

Simplifying
x = -2.16002735945

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.01717021655, -2.16002735945}
Solution
x = {2.01717021655, -2.16002735945}