(6x+8)(7x-4)=90

Solution for (6x+8)(7x-4)=90 equation:

Simplifying
(6x + 8)(7x + -4) = 90

Reorder the terms:
(8 + 6x)(7x + -4) = 90

Reorder the terms:
(8 + 6x)(-4 + 7x) = 90

Multiply (8 + 6x) * (-4 + 7x)
(8(-4 + 7x) + 6x * (-4 + 7x)) = 90
((-4 * 8 + 7x * 8) + 6x * (-4 + 7x)) = 90
((-32 + 56x) + 6x * (-4 + 7x)) = 90
(-32 + 56x + (-4 * 6x + 7x * 6x)) = 90
(-32 + 56x + (-24x + 42x2)) = 90

Combine like terms: 56x + -24x = 32x
(-32 + 32x + 42x2) = 90

Solving
-32 + 32x + 42x2 = 90

Solving for variable 'x'.

Reorder the terms:
-32 + -90 + 32x + 42x2 = 90 + -90

Combine like terms: -32 + -90 = -122
-122 + 32x + 42x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-122 + 32x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + 16x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-61 + 16x + 21x2)' equal to zero and attempt to solve:

Simplifying
-61 + 16x + 21x2 = 0

Solving
-61 + 16x + 21x2 = 0

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

Divide each side by '21'.
-2.904761905 + 0.7619047619x + x2 = 0

Move the constant term to the right:

Add '2.904761905' to each side of the equation.
-2.904761905 + 0.7619047619x + 2.904761905 + x2 = 0 + 2.904761905

Reorder the terms:
-2.904761905 + 2.904761905 + 0.7619047619x + x2 = 0 + 2.904761905

Combine like terms: -2.904761905 + 2.904761905 = 0.000000000
0.000000000 + 0.7619047619x + x2 = 0 + 2.904761905
0.7619047619x + x2 = 0 + 2.904761905

Combine like terms: 0 + 2.904761905 = 2.904761905
0.7619047619x + x2 = 2.904761905

The x term is 0.7619047619x.  Take half its coefficient (0.380952381).
Square it (0.1451247166) and add it to both sides.

Add '0.1451247166' to each side of the equation.
0.7619047619x + 0.1451247166 + x2 = 2.904761905 + 0.1451247166

Reorder the terms:
0.1451247166 + 0.7619047619x + x2 = 2.904761905 + 0.1451247166

Combine like terms: 2.904761905 + 0.1451247166 = 3.0498866216
0.1451247166 + 0.7619047619x + x2 = 3.0498866216

Factor a perfect square on the left side:
(x + 0.380952381)(x + 0.380952381) = 3.0498866216

Calculate the square root of the right side: 1.746392459

Break this problem into two subproblems by setting 
(x + 0.380952381) equal to 1.746392459 and -1.746392459.

Subproblem 1
x + 0.380952381 = 1.746392459

Simplifying
x + 0.380952381 = 1.746392459

Reorder the terms:
0.380952381 + x = 1.746392459

Solving
0.380952381 + x = 1.746392459

Solving for variable 'x'.

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

Add '-0.380952381' to each side of the equation.
0.380952381 + -0.380952381 + x = 1.746392459 + -0.380952381

Combine like terms: 0.380952381 + -0.380952381 = 0.000000000
0.000000000 + x = 1.746392459 + -0.380952381
x = 1.746392459 + -0.380952381

Combine like terms: 1.746392459 + -0.380952381 = 1.365440078
x = 1.365440078

Simplifying
x = 1.365440078

Subproblem 2
x + 0.380952381 = -1.746392459

Simplifying
x + 0.380952381 = -1.746392459

Reorder the terms:
0.380952381 + x = -1.746392459

Solving
0.380952381 + x = -1.746392459

Solving for variable 'x'.

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

Add '-0.380952381' to each side of the equation.
0.380952381 + -0.380952381 + x = -1.746392459 + -0.380952381

Combine like terms: 0.380952381 + -0.380952381 = 0.000000000
0.000000000 + x = -1.746392459 + -0.380952381
x = -1.746392459 + -0.380952381

Combine like terms: -1.746392459 + -0.380952381 = -2.12734484
x = -2.12734484

Simplifying
x = -2.12734484

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.365440078, -2.12734484}
Solution
x = {1.365440078, -2.12734484}