(2x-8)(7x+5)=8

Solution for (2x-8)(7x+5)=8 equation:

Simplifying
(2x + -8)(7x + 5) = 8

Reorder the terms:
(-8 + 2x)(7x + 5) = 8

Reorder the terms:
(-8 + 2x)(5 + 7x) = 8

Multiply (-8 + 2x) * (5 + 7x)
(-8(5 + 7x) + 2x * (5 + 7x)) = 8
((5 * -8 + 7x * -8) + 2x * (5 + 7x)) = 8
((-40 + -56x) + 2x * (5 + 7x)) = 8
(-40 + -56x + (5 * 2x + 7x * 2x)) = 8
(-40 + -56x + (10x + 14x2)) = 8

Combine like terms: -56x + 10x = -46x
(-40 + -46x + 14x2) = 8

Solving
-40 + -46x + 14x2 = 8

Solving for variable 'x'.

Reorder the terms:
-40 + -8 + -46x + 14x2 = 8 + -8

Combine like terms: -40 + -8 = -48
-48 + -46x + 14x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-48 + -46x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -23x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -23x + 7x2)' equal to zero and attempt to solve:

Simplifying
-24 + -23x + 7x2 = 0

Solving
-24 + -23x + 7x2 = 0

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

Divide each side by '7'.
-3.428571429 + -3.285714286x + x2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + -3.285714286x + 3.428571429 + x2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + -3.285714286x + x2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + -3.285714286x + x2 = 0 + 3.428571429
-3.285714286x + x2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
-3.285714286x + x2 = 3.428571429

The x term is -3.285714286x.  Take half its coefficient (-1.642857143).
Square it (2.698979592) and add it to both sides.

Add '2.698979592' to each side of the equation.
-3.285714286x + 2.698979592 + x2 = 3.428571429 + 2.698979592

Reorder the terms:
2.698979592 + -3.285714286x + x2 = 3.428571429 + 2.698979592

Combine like terms: 3.428571429 + 2.698979592 = 6.127551021
2.698979592 + -3.285714286x + x2 = 6.127551021

Factor a perfect square on the left side:
(x + -1.642857143)(x + -1.642857143) = 6.127551021

Calculate the square root of the right side: 2.475389065

Break this problem into two subproblems by setting 
(x + -1.642857143) equal to 2.475389065 and -2.475389065.

Subproblem 1
x + -1.642857143 = 2.475389065

Simplifying
x + -1.642857143 = 2.475389065

Reorder the terms:
-1.642857143 + x = 2.475389065

Solving
-1.642857143 + x = 2.475389065

Solving for variable 'x'.

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

Add '1.642857143' to each side of the equation.
-1.642857143 + 1.642857143 + x = 2.475389065 + 1.642857143

Combine like terms: -1.642857143 + 1.642857143 = 0.000000000
0.000000000 + x = 2.475389065 + 1.642857143
x = 2.475389065 + 1.642857143

Combine like terms: 2.475389065 + 1.642857143 = 4.118246208
x = 4.118246208

Simplifying
x = 4.118246208

Subproblem 2
x + -1.642857143 = -2.475389065

Simplifying
x + -1.642857143 = -2.475389065

Reorder the terms:
-1.642857143 + x = -2.475389065

Solving
-1.642857143 + x = -2.475389065

Solving for variable 'x'.

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

Add '1.642857143' to each side of the equation.
-1.642857143 + 1.642857143 + x = -2.475389065 + 1.642857143

Combine like terms: -1.642857143 + 1.642857143 = 0.000000000
0.000000000 + x = -2.475389065 + 1.642857143
x = -2.475389065 + 1.642857143

Combine like terms: -2.475389065 + 1.642857143 = -0.832531922
x = -0.832531922

Simplifying
x = -0.832531922

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.118246208, -0.832531922}
Solution
x = {4.118246208, -0.832531922}