(6x+6)(6x+8)=141

Solution for (6x+6)(6x+8)=141 equation:

Simplifying
(6x + 6)(6x + 8) = 141

Reorder the terms:
(6 + 6x)(6x + 8) = 141

Reorder the terms:
(6 + 6x)(8 + 6x) = 141

Multiply (6 + 6x) * (8 + 6x)
(6(8 + 6x) + 6x * (8 + 6x)) = 141
((8 * 6 + 6x * 6) + 6x * (8 + 6x)) = 141
((48 + 36x) + 6x * (8 + 6x)) = 141
(48 + 36x + (8 * 6x + 6x * 6x)) = 141
(48 + 36x + (48x + 36x2)) = 141

Combine like terms: 36x + 48x = 84x
(48 + 84x + 36x2) = 141

Solving
48 + 84x + 36x2 = 141

Solving for variable 'x'.

Reorder the terms:
48 + -141 + 84x + 36x2 = 141 + -141

Combine like terms: 48 + -141 = -93
-93 + 84x + 36x2 = 141 + -141

Combine like terms: 141 + -141 = 0
-93 + 84x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-31 + 28x + 12x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-31 + 28x + 12x2)' equal to zero and attempt to solve:

Simplifying
-31 + 28x + 12x2 = 0

Solving
-31 + 28x + 12x2 = 0

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

Divide each side by '12'.
-2.583333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.583333333' to each side of the equation.
-2.583333333 + 2.333333333x + 2.583333333 + x2 = 0 + 2.583333333

Reorder the terms:
-2.583333333 + 2.583333333 + 2.333333333x + x2 = 0 + 2.583333333

Combine like terms: -2.583333333 + 2.583333333 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 2.583333333
2.333333333x + x2 = 0 + 2.583333333

Combine like terms: 0 + 2.583333333 = 2.583333333
2.333333333x + x2 = 2.583333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 2.583333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 2.583333333 + 1.361111112

Combine like terms: 2.583333333 + 1.361111112 = 3.944444445
1.361111112 + 2.333333333x + x2 = 3.944444445

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 3.944444445

Calculate the square root of the right side: 1.986062548

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.986062548 and -1.986062548.

Subproblem 1
x + 1.166666667 = 1.986062548

Simplifying
x + 1.166666667 = 1.986062548

Reorder the terms:
1.166666667 + x = 1.986062548

Solving
1.166666667 + x = 1.986062548

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.986062548 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.986062548 + -1.166666667
x = 1.986062548 + -1.166666667

Combine like terms: 1.986062548 + -1.166666667 = 0.819395881
x = 0.819395881

Simplifying
x = 0.819395881

Subproblem 2
x + 1.166666667 = -1.986062548

Simplifying
x + 1.166666667 = -1.986062548

Reorder the terms:
1.166666667 + x = -1.986062548

Solving
1.166666667 + x = -1.986062548

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.986062548 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.986062548 + -1.166666667
x = -1.986062548 + -1.166666667

Combine like terms: -1.986062548 + -1.166666667 = -3.152729215
x = -3.152729215

Simplifying
x = -3.152729215

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.819395881, -3.152729215}
Solution
x = {0.819395881, -3.152729215}