(8x-8)(7x+8)=90

Solution for (8x-8)(7x+8)=90 equation:

Simplifying
(8x + -8)(7x + 8) = 90

Reorder the terms:
(-8 + 8x)(7x + 8) = 90

Reorder the terms:
(-8 + 8x)(8 + 7x) = 90

Multiply (-8 + 8x) * (8 + 7x)
(-8(8 + 7x) + 8x * (8 + 7x)) = 90
((8 * -8 + 7x * -8) + 8x * (8 + 7x)) = 90
((-64 + -56x) + 8x * (8 + 7x)) = 90
(-64 + -56x + (8 * 8x + 7x * 8x)) = 90
(-64 + -56x + (64x + 56x2)) = 90

Combine like terms: -56x + 64x = 8x
(-64 + 8x + 56x2) = 90

Solving
-64 + 8x + 56x2 = 90

Solving for variable 'x'.

Reorder the terms:
-64 + -90 + 8x + 56x2 = 90 + -90

Combine like terms: -64 + -90 = -154
-154 + 8x + 56x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-154 + 8x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-77 + 4x + 28x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-77 + 4x + 28x2)' equal to zero and attempt to solve:

Simplifying
-77 + 4x + 28x2 = 0

Solving
-77 + 4x + 28x2 = 0

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

Divide each side by '28'.
-2.75 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 0.1428571429x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 0.1428571429x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 0.1428571429x + x2 = 0 + 2.75
0.1428571429x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
0.1428571429x + x2 = 2.75

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 = 2.75 + 0.005102040819

Reorder the terms:
0.005102040819 + 0.1428571429x + x2 = 2.75 + 0.005102040819

Combine like terms: 2.75 + 0.005102040819 = 2.755102040819
0.005102040819 + 0.1428571429x + x2 = 2.755102040819

Factor a perfect square on the left side:
(x + 0.07142857145)(x + 0.07142857145) = 2.755102040819

Calculate the square root of the right side: 1.659850006

Break this problem into two subproblems by setting 
(x + 0.07142857145) equal to 1.659850006 and -1.659850006.

Subproblem 1
x + 0.07142857145 = 1.659850006

Simplifying
x + 0.07142857145 = 1.659850006

Reorder the terms:
0.07142857145 + x = 1.659850006

Solving
0.07142857145 + x = 1.659850006

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 = 1.659850006 + -0.07142857145

Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000
0.00000000000 + x = 1.659850006 + -0.07142857145
x = 1.659850006 + -0.07142857145

Combine like terms: 1.659850006 + -0.07142857145 = 1.58842143455
x = 1.58842143455

Simplifying
x = 1.58842143455

Subproblem 2
x + 0.07142857145 = -1.659850006

Simplifying
x + 0.07142857145 = -1.659850006

Reorder the terms:
0.07142857145 + x = -1.659850006

Solving
0.07142857145 + x = -1.659850006

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 = -1.659850006 + -0.07142857145

Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000
0.00000000000 + x = -1.659850006 + -0.07142857145
x = -1.659850006 + -0.07142857145

Combine like terms: -1.659850006 + -0.07142857145 = -1.73127857745
x = -1.73127857745

Simplifying
x = -1.73127857745

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.58842143455, -1.73127857745}
Solution
x = {1.58842143455, -1.73127857745}