(6x+2)(6x+2)=60

Solution for (6x+2)(6x+2)=60 equation:

Simplifying
(6x + 2)(6x + 2) = 60

Reorder the terms:
(2 + 6x)(6x + 2) = 60

Reorder the terms:
(2 + 6x)(2 + 6x) = 60

Multiply (2 + 6x) * (2 + 6x)
(2(2 + 6x) + 6x * (2 + 6x)) = 60
((2 * 2 + 6x * 2) + 6x * (2 + 6x)) = 60
((4 + 12x) + 6x * (2 + 6x)) = 60
(4 + 12x + (2 * 6x + 6x * 6x)) = 60
(4 + 12x + (12x + 36x2)) = 60

Combine like terms: 12x + 12x = 24x
(4 + 24x + 36x2) = 60

Solving
4 + 24x + 36x2 = 60

Solving for variable 'x'.

Reorder the terms:
4 + -60 + 24x + 36x2 = 60 + -60

Combine like terms: 4 + -60 = -56
-56 + 24x + 36x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-56 + 24x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 6x + 9x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-14 + 6x + 9x2)' equal to zero and attempt to solve:

Simplifying
-14 + 6x + 9x2 = 0

Solving
-14 + 6x + 9x2 = 0

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

Divide each side by '9'.
-1.555555556 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + 0.6666666667x + 1.555555556 + x2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + 0.6666666667x + x2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.555555556
0.6666666667x + x2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
0.6666666667x + x2 = 1.555555556

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.555555556 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.555555556 + 0.1111111112

Combine like terms: 1.555555556 + 0.1111111112 = 1.6666666672
0.1111111112 + 0.6666666667x + x2 = 1.6666666672

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.6666666672

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.290994449 and -1.290994449.

Subproblem 1
x + 0.3333333334 = 1.290994449

Simplifying
x + 0.3333333334 = 1.290994449

Reorder the terms:
0.3333333334 + x = 1.290994449

Solving
0.3333333334 + x = 1.290994449

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.290994449 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.290994449 + -0.3333333334
x = 1.290994449 + -0.3333333334

Combine like terms: 1.290994449 + -0.3333333334 = 0.9576611156
x = 0.9576611156

Simplifying
x = 0.9576611156

Subproblem 2
x + 0.3333333334 = -1.290994449

Simplifying
x + 0.3333333334 = -1.290994449

Reorder the terms:
0.3333333334 + x = -1.290994449

Solving
0.3333333334 + x = -1.290994449

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.290994449 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.290994449 + -0.3333333334
x = -1.290994449 + -0.3333333334

Combine like terms: -1.290994449 + -0.3333333334 = -1.6243277824
x = -1.6243277824

Simplifying
x = -1.6243277824

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9576611156, -1.6243277824}
Solution
x = {0.9576611156, -1.6243277824}