(2x-1)(3x+6)=90

Solution for (2x-1)(3x+6)=90 equation:

Simplifying
(2x + -1)(3x + 6) = 90

Reorder the terms:
(-1 + 2x)(3x + 6) = 90

Reorder the terms:
(-1 + 2x)(6 + 3x) = 90

Multiply (-1 + 2x) * (6 + 3x)
(-1(6 + 3x) + 2x * (6 + 3x)) = 90
((6 * -1 + 3x * -1) + 2x * (6 + 3x)) = 90
((-6 + -3x) + 2x * (6 + 3x)) = 90
(-6 + -3x + (6 * 2x + 3x * 2x)) = 90
(-6 + -3x + (12x + 6x2)) = 90

Combine like terms: -3x + 12x = 9x
(-6 + 9x + 6x2) = 90

Solving
-6 + 9x + 6x2 = 90

Solving for variable 'x'.

Reorder the terms:
-6 + -90 + 9x + 6x2 = 90 + -90

Combine like terms: -6 + -90 = -96
-96 + 9x + 6x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-96 + 9x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-32 + 3x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-32 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-32 + 3x + 2x2 = 0

Solving
-32 + 3x + 2x2 = 0

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

Divide each side by '2'.
-16 + 1.5x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 1.5x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 1.5x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 1.5x + x2 = 0 + 16
1.5x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
1.5x + x2 = 16

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 16 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 16 + 0.5625

Combine like terms: 16 + 0.5625 = 16.5625
0.5625 + 1.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + 0.75) equal to 4.069705149 and -4.069705149.

Subproblem 1
x + 0.75 = 4.069705149

Simplifying
x + 0.75 = 4.069705149

Reorder the terms:
0.75 + x = 4.069705149

Solving
0.75 + x = 4.069705149

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 4.069705149 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 4.069705149 + -0.75
x = 4.069705149 + -0.75

Combine like terms: 4.069705149 + -0.75 = 3.319705149
x = 3.319705149

Simplifying
x = 3.319705149

Subproblem 2
x + 0.75 = -4.069705149

Simplifying
x + 0.75 = -4.069705149

Reorder the terms:
0.75 + x = -4.069705149

Solving
0.75 + x = -4.069705149

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -4.069705149 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -4.069705149 + -0.75
x = -4.069705149 + -0.75

Combine like terms: -4.069705149 + -0.75 = -4.819705149
x = -4.819705149

Simplifying
x = -4.819705149

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.319705149, -4.819705149}
Solution
x = {3.319705149, -4.819705149}