(7x+6)(5x)=90

Solution for (7x+6)(5x)=90 equation:

Simplifying
(7x + 6)(5x) = 90

Reorder the terms:
(6 + 7x)(5x) = 90

Remove parenthesis around (5x)
(6 + 7x) * 5x = 90

Reorder the terms for easier multiplication:
5x(6 + 7x) = 90
(6 * 5x + 7x * 5x) = 90
(30x + 35x2) = 90

Solving
30x + 35x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 30x + 35x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 30x + 35x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + 6x + 7x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-18 + 6x + 7x2)' equal to zero and attempt to solve:

Simplifying
-18 + 6x + 7x2 = 0

Solving
-18 + 6x + 7x2 = 0

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

Divide each side by '7'.
-2.571428571 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + 0.8571428571x + 2.571428571 + x2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + 0.8571428571x + x2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + 0.8571428571x + x2 = 0 + 2.571428571
0.8571428571x + x2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
0.8571428571x + x2 = 2.571428571

The x term is 0.8571428571x.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571x + 0.1836734694 + x2 = 2.571428571 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 2.571428571 + 0.1836734694

Combine like terms: 2.571428571 + 0.1836734694 = 2.7551020404
0.1836734694 + 0.8571428571x + x2 = 2.7551020404

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 2.7551020404

Calculate the square root of the right side: 1.659850005

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 1.659850005 and -1.659850005.

Subproblem 1
x + 0.4285714286 = 1.659850005

Simplifying
x + 0.4285714286 = 1.659850005

Reorder the terms:
0.4285714286 + x = 1.659850005

Solving
0.4285714286 + x = 1.659850005

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = 1.659850005 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = 1.659850005 + -0.4285714286
x = 1.659850005 + -0.4285714286

Combine like terms: 1.659850005 + -0.4285714286 = 1.2312785764
x = 1.2312785764

Simplifying
x = 1.2312785764

Subproblem 2
x + 0.4285714286 = -1.659850005

Simplifying
x + 0.4285714286 = -1.659850005

Reorder the terms:
0.4285714286 + x = -1.659850005

Solving
0.4285714286 + x = -1.659850005

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = -1.659850005 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = -1.659850005 + -0.4285714286
x = -1.659850005 + -0.4285714286

Combine like terms: -1.659850005 + -0.4285714286 = -2.0884214336
x = -2.0884214336

Simplifying
x = -2.0884214336

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2312785764, -2.0884214336}
Solution
x = {1.2312785764, -2.0884214336}