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

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

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

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

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

Multiply (2 + 3x) * (6 + 6x)
90 = (2(6 + 6x) + 3x * (6 + 6x))
90 = ((6 * 2 + 6x * 2) + 3x * (6 + 6x))
90 = ((12 + 12x) + 3x * (6 + 6x))
90 = (12 + 12x + (6 * 3x + 6x * 3x))
90 = (12 + 12x + (18x + 18x2))

Combine like terms: 12x + 18x = 30x
90 = (12 + 30x + 18x2)

Solving
90 = 12 + 30x + 18x2

Solving for variable 'x'.

Combine like terms: 90 + -12 = 78
78 + -30x + -18x2 = 12 + 30x + 18x2 + -12 + -30x + -18x2

Reorder the terms:
78 + -30x + -18x2 = 12 + -12 + 30x + -30x + 18x2 + -18x2

Combine like terms: 12 + -12 = 0
78 + -30x + -18x2 = 0 + 30x + -30x + 18x2 + -18x2
78 + -30x + -18x2 = 30x + -30x + 18x2 + -18x2

Combine like terms: 30x + -30x = 0
78 + -30x + -18x2 = 0 + 18x2 + -18x2
78 + -30x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
78 + -30x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(13 + -5x + -3x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(13 + -5x + -3x2)' equal to zero and attempt to solve:

Simplifying
13 + -5x + -3x2 = 0

Solving
13 + -5x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 1.666666667x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 1.666666667x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 4.333333333
1.666666667x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
1.666666667x + x2 = 4.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 4.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 4.333333333 + 0.6944444447

Combine like terms: 4.333333333 + 0.6944444447 = 5.0277777777
0.6944444447 + 1.666666667x + x2 = 5.0277777777

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 5.0277777777

Calculate the square root of the right side: 2.242270674

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.242270674 and -2.242270674.

Subproblem 1
x + 0.8333333335 = 2.242270674

Simplifying
x + 0.8333333335 = 2.242270674

Reorder the terms:
0.8333333335 + x = 2.242270674

Solving
0.8333333335 + x = 2.242270674

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.242270674 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.242270674 + -0.8333333335
x = 2.242270674 + -0.8333333335

Combine like terms: 2.242270674 + -0.8333333335 = 1.4089373405
x = 1.4089373405

Simplifying
x = 1.4089373405

Subproblem 2
x + 0.8333333335 = -2.242270674

Simplifying
x + 0.8333333335 = -2.242270674

Reorder the terms:
0.8333333335 + x = -2.242270674

Solving
0.8333333335 + x = -2.242270674

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.242270674 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.242270674 + -0.8333333335
x = -2.242270674 + -0.8333333335

Combine like terms: -2.242270674 + -0.8333333335 = -3.0756040075
x = -3.0756040075

Simplifying
x = -3.0756040075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4089373405, -3.0756040075}
Solution
x = {1.4089373405, -3.0756040075}