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

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

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

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

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

Multiply (6 + 2x) * (6 + 2x)
(6(6 + 2x) + 2x * (6 + 2x)) = 6
((6 * 6 + 2x * 6) + 2x * (6 + 2x)) = 6
((36 + 12x) + 2x * (6 + 2x)) = 6
(36 + 12x + (6 * 2x + 2x * 2x)) = 6
(36 + 12x + (12x + 4x2)) = 6

Combine like terms: 12x + 12x = 24x
(36 + 24x + 4x2) = 6

Solving
36 + 24x + 4x2 = 6

Solving for variable 'x'.

Reorder the terms:
36 + -6 + 24x + 4x2 = 6 + -6

Combine like terms: 36 + -6 = 30
30 + 24x + 4x2 = 6 + -6

Combine like terms: 6 + -6 = 0
30 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 12x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + 12x + 2x2)' equal to zero and attempt to solve:

Simplifying
15 + 12x + 2x2 = 0

Solving
15 + 12x + 2x2 = 0

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

Divide each side by '2'.
7.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + 6x + -7.5 + x2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + 6x + x2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + 6x + x2 = 0 + -7.5
6x + x2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
6x + x2 = -7.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -7.5 + 9

Reorder the terms:
9 + 6x + x2 = -7.5 + 9

Combine like terms: -7.5 + 9 = 1.5
9 + 6x + x2 = 1.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + 3) equal to 1.224744871 and -1.224744871.

Subproblem 1
x + 3 = 1.224744871

Simplifying
x + 3 = 1.224744871

Reorder the terms:
3 + x = 1.224744871

Solving
3 + x = 1.224744871

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.224744871 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.224744871 + -3
x = 1.224744871 + -3

Combine like terms: 1.224744871 + -3 = -1.775255129
x = -1.775255129

Simplifying
x = -1.775255129

Subproblem 2
x + 3 = -1.224744871

Simplifying
x + 3 = -1.224744871

Reorder the terms:
3 + x = -1.224744871

Solving
3 + x = -1.224744871

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.224744871 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.224744871 + -3
x = -1.224744871 + -3

Combine like terms: -1.224744871 + -3 = -4.224744871
x = -4.224744871

Simplifying
x = -4.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.775255129, -4.224744871}
Solution
x = {-1.775255129, -4.224744871}