(4x+2)(9x-3)=90

Solution for (4x+2)(9x-3)=90 equation:

Simplifying
(4x + 2)(9x + -3) = 90

Reorder the terms:
(2 + 4x)(9x + -3) = 90

Reorder the terms:
(2 + 4x)(-3 + 9x) = 90

Multiply (2 + 4x) * (-3 + 9x)
(2(-3 + 9x) + 4x * (-3 + 9x)) = 90
((-3 * 2 + 9x * 2) + 4x * (-3 + 9x)) = 90
((-6 + 18x) + 4x * (-3 + 9x)) = 90
(-6 + 18x + (-3 * 4x + 9x * 4x)) = 90
(-6 + 18x + (-12x + 36x2)) = 90

Combine like terms: 18x + -12x = 6x
(-6 + 6x + 36x2) = 90

Solving
-6 + 6x + 36x2 = 90

Solving for variable 'x'.

Reorder the terms:
-6 + -90 + 6x + 36x2 = 90 + -90

Combine like terms: -6 + -90 = -96
-96 + 6x + 36x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-96 + 6x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-16 + x + 6x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-16 + x + 6x2)' equal to zero and attempt to solve:

Simplifying
-16 + x + 6x2 = 0

Solving
-16 + x + 6x2 = 0

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

Divide each side by '6'.
-2.666666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 0.1666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 0.1666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + 2.666666667
0.1666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
0.1666666667x + x2 = 2.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 2.666666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
0.25 + 0.1666666667x + x2 = 2.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.707825128 and -1.707825128.

Subproblem 1
x + 0.5 = 1.707825128

Simplifying
x + 0.5 = 1.707825128

Reorder the terms:
0.5 + x = 1.707825128

Solving
0.5 + x = 1.707825128

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.707825128 + -0.5
x = 1.707825128 + -0.5

Combine like terms: 1.707825128 + -0.5 = 1.207825128
x = 1.207825128

Simplifying
x = 1.207825128

Subproblem 2
x + 0.5 = -1.707825128

Simplifying
x + 0.5 = -1.707825128

Reorder the terms:
0.5 + x = -1.707825128

Solving
0.5 + x = -1.707825128

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.707825128 + -0.5
x = -1.707825128 + -0.5

Combine like terms: -1.707825128 + -0.5 = -2.207825128
x = -2.207825128

Simplifying
x = -2.207825128

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.207825128, -2.207825128}
Solution
x = {1.207825128, -2.207825128}