2x(4x-6)=90

Solution for 2x(4x-6)=90 equation:

Simplifying
2x(4x + -6) = 90

Reorder the terms:
2x(-6 + 4x) = 90
(-6 * 2x + 4x * 2x) = 90
(-12x + 8x2) = 90

Solving
-12x + 8x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -12x + 8x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -12x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -6x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + -6x + 4x2)' equal to zero and attempt to solve:

Simplifying
-45 + -6x + 4x2 = 0

Solving
-45 + -6x + 4x2 = 0

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

Divide each side by '4'.
-11.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -1.5x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -1.5x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -1.5x + x2 = 0 + 11.25
-1.5x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-1.5x + x2 = 11.25

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 = 11.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 11.25 + 0.5625

Combine like terms: 11.25 + 0.5625 = 11.8125
0.5625 + -1.5x + x2 = 11.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 11.8125

Calculate the square root of the right side: 3.436931771

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.436931771 and -3.436931771.

Subproblem 1
x + -0.75 = 3.436931771

Simplifying
x + -0.75 = 3.436931771

Reorder the terms:
-0.75 + x = 3.436931771

Solving
-0.75 + x = 3.436931771

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 = 3.436931771 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.436931771 + 0.75
x = 3.436931771 + 0.75

Combine like terms: 3.436931771 + 0.75 = 4.186931771
x = 4.186931771

Simplifying
x = 4.186931771

Subproblem 2
x + -0.75 = -3.436931771

Simplifying
x + -0.75 = -3.436931771

Reorder the terms:
-0.75 + x = -3.436931771

Solving
-0.75 + x = -3.436931771

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 = -3.436931771 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.436931771 + 0.75
x = -3.436931771 + 0.75

Combine like terms: -3.436931771 + 0.75 = -2.686931771
x = -2.686931771

Simplifying
x = -2.686931771

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.186931771, -2.686931771}
Solution
x = {4.186931771, -2.686931771}