90=(3x+6)(4x)

Solution for 90=(3x+6)(4x) equation:

Simplifying
90 = (3x + 6)(4x)

Reorder the terms:
90 = (6 + 3x)(4x)

Remove parenthesis around (4x)
90 = (6 + 3x) * 4x

Reorder the terms for easier multiplication:
90 = 4x(6 + 3x)
90 = (6 * 4x + 3x * 4x)
90 = (24x + 12x2)

Solving
90 = 24x + 12x2

Solving for variable 'x'.

Reorder the terms:
90 + -24x + -12x2 = 24x + -24x + 12x2 + -12x2

Combine like terms: 24x + -24x = 0
90 + -24x + -12x2 = 0 + 12x2 + -12x2
90 + -24x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
90 + -24x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + -4x + -2x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(15 + -4x + -2x2)' equal to zero and attempt to solve:

Simplifying
15 + -4x + -2x2 = 0

Solving
15 + -4x + -2x2 = 0

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

Divide each side by '-2'.
-7.5 + 2x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 2x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 2x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 2x + x2 = 0 + 7.5
2x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
2x + x2 = 7.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 7.5 + 1

Reorder the terms:
1 + 2x + x2 = 7.5 + 1

Combine like terms: 7.5 + 1 = 8.5
1 + 2x + x2 = 8.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + 1) equal to 2.915475947 and -2.915475947.

Subproblem 1
x + 1 = 2.915475947

Simplifying
x + 1 = 2.915475947

Reorder the terms:
1 + x = 2.915475947

Solving
1 + x = 2.915475947

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.915475947 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.915475947 + -1
x = 2.915475947 + -1

Combine like terms: 2.915475947 + -1 = 1.915475947
x = 1.915475947

Simplifying
x = 1.915475947

Subproblem 2
x + 1 = -2.915475947

Simplifying
x + 1 = -2.915475947

Reorder the terms:
1 + x = -2.915475947

Solving
1 + x = -2.915475947

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.915475947 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.915475947 + -1
x = -2.915475947 + -1

Combine like terms: -2.915475947 + -1 = -3.915475947
x = -3.915475947

Simplifying
x = -3.915475947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.915475947, -3.915475947}
Solution
x = {1.915475947, -3.915475947}