(6x)(6x)+2x-32=0

Solution for (6x)(6x)+2x-32=0 equation:

Simplifying
(6x)(6x) + 2x + -32 = 0

Remove parenthesis around (6x)
6x(6x) + 2x + -32 = 0

Remove parenthesis around (6x)
6x * 6x + 2x + -32 = 0

Reorder the terms for easier multiplication:
6 * 6x * x + 2x + -32 = 0

Multiply 6 * 6
36x * x + 2x + -32 = 0

Multiply x * x
36x2 + 2x + -32 = 0

Reorder the terms:
-32 + 2x + 36x2 = 0

Solving
-32 + 2x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + x + 18x2)' equal to zero and attempt to solve:

Simplifying
-16 + x + 18x2 = 0

Solving
-16 + x + 18x2 = 0

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

Divide each side by '18'.
-0.8888888889 + 0.05555555556x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 0.05555555556x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 0.05555555556x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 0.05555555556x + x2 = 0 + 0.8888888889
0.05555555556x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
0.05555555556x + x2 = 0.8888888889

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.05555555556x + 0.25 + x2 = 0.8888888889 + 0.25

Reorder the terms:
0.25 + 0.05555555556x + x2 = 0.8888888889 + 0.25

Combine like terms: 0.8888888889 + 0.25 = 1.1388888889
0.25 + 0.05555555556x + x2 = 1.1388888889

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.1388888889

Calculate the square root of the right side: 1.067187373

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.067187373 and -1.067187373.

Subproblem 1
x + 0.5 = 1.067187373

Simplifying
x + 0.5 = 1.067187373

Reorder the terms:
0.5 + x = 1.067187373

Solving
0.5 + x = 1.067187373

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.067187373 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.067187373 + -0.5
x = 1.067187373 + -0.5

Combine like terms: 1.067187373 + -0.5 = 0.567187373
x = 0.567187373

Simplifying
x = 0.567187373

Subproblem 2
x + 0.5 = -1.067187373

Simplifying
x + 0.5 = -1.067187373

Reorder the terms:
0.5 + x = -1.067187373

Solving
0.5 + x = -1.067187373

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.067187373 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.067187373 + -0.5
x = -1.067187373 + -0.5

Combine like terms: -1.067187373 + -0.5 = -1.567187373
x = -1.567187373

Simplifying
x = -1.567187373

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.567187373, -1.567187373}
Solution
x = {0.567187373, -1.567187373}