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

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

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

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

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

Multiply (6 + x) * (6 + x)
2(6(6 + x) + x(6 + x)) = 90
2((6 * 6 + x * 6) + x(6 + x)) = 90
2((36 + 6x) + x(6 + x)) = 90
2(36 + 6x + (6 * x + x * x)) = 90
2(36 + 6x + (6x + x2)) = 90

Combine like terms: 6x + 6x = 12x
2(36 + 12x + x2) = 90
(36 * 2 + 12x * 2 + x2 * 2) = 90
(72 + 24x + 2x2) = 90

Solving
72 + 24x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
72 + -90 + 24x + 2x2 = 90 + -90

Combine like terms: 72 + -90 = -18
-18 + 24x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-18 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 12x + x2 = 0

Solving
-9 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 12x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 12x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 12x + x2 = 0 + 9
12x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
12x + x2 = 9

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 9 + 36

Reorder the terms:
36 + 12x + x2 = 9 + 36

Combine like terms: 9 + 36 = 45
36 + 12x + x2 = 45

Factor a perfect square on the left side:
(x + 6)(x + 6) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 6) equal to 6.708203933 and -6.708203933.

Subproblem 1
x + 6 = 6.708203933

Simplifying
x + 6 = 6.708203933

Reorder the terms:
6 + x = 6.708203933

Solving
6 + x = 6.708203933

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 6.708203933 + -6

Combine like terms: 6 + -6 = 0
0 + x = 6.708203933 + -6
x = 6.708203933 + -6

Combine like terms: 6.708203933 + -6 = 0.708203933
x = 0.708203933

Simplifying
x = 0.708203933

Subproblem 2
x + 6 = -6.708203933

Simplifying
x + 6 = -6.708203933

Reorder the terms:
6 + x = -6.708203933

Solving
6 + x = -6.708203933

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -6.708203933 + -6

Combine like terms: 6 + -6 = 0
0 + x = -6.708203933 + -6
x = -6.708203933 + -6

Combine like terms: -6.708203933 + -6 = -12.708203933
x = -12.708203933

Simplifying
x = -12.708203933

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.708203933, -12.708203933}
Solution
x = {0.708203933, -12.708203933}