(6x-4)(6x-4)=6

Solution for (6x-4)(6x-4)=6 equation:

Simplifying
(6x + -4)(6x + -4) = 6

Reorder the terms:
(-4 + 6x)(6x + -4) = 6

Reorder the terms:
(-4 + 6x)(-4 + 6x) = 6

Multiply (-4 + 6x) * (-4 + 6x)
(-4(-4 + 6x) + 6x * (-4 + 6x)) = 6
((-4 * -4 + 6x * -4) + 6x * (-4 + 6x)) = 6
((16 + -24x) + 6x * (-4 + 6x)) = 6
(16 + -24x + (-4 * 6x + 6x * 6x)) = 6
(16 + -24x + (-24x + 36x2)) = 6

Combine like terms: -24x + -24x = -48x
(16 + -48x + 36x2) = 6

Solving
16 + -48x + 36x2 = 6

Solving for variable 'x'.

Reorder the terms:
16 + -6 + -48x + 36x2 = 6 + -6

Combine like terms: 16 + -6 = 10
10 + -48x + 36x2 = 6 + -6

Combine like terms: 6 + -6 = 0
10 + -48x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -24x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -24x + 18x2)' equal to zero and attempt to solve:

Simplifying
5 + -24x + 18x2 = 0

Solving
5 + -24x + 18x2 = 0

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

Divide each side by '18'.
0.2777777778 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -1.333333333x + -0.2777777778 + x2 = 0 + -0.2777777778

Reorder the terms:
0.2777777778 + -0.2777777778 + -1.333333333x + x2 = 0 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + -0.2777777778
-1.333333333x + x2 = 0 + -0.2777777778

Combine like terms: 0 + -0.2777777778 = -0.2777777778
-1.333333333x + x2 = -0.2777777778

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -0.2777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -0.2777777778 + 0.4444444442

Combine like terms: -0.2777777778 + 0.4444444442 = 0.1666666664
0.4444444442 + -1.333333333x + x2 = 0.1666666664

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.1666666664

Calculate the square root of the right side: 0.40824829

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.40824829 and -0.40824829.

Subproblem 1
x + -0.6666666665 = 0.40824829

Simplifying
x + -0.6666666665 = 0.40824829

Reorder the terms:
-0.6666666665 + x = 0.40824829

Solving
-0.6666666665 + x = 0.40824829

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 0.40824829 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 0.40824829 + 0.6666666665
x = 0.40824829 + 0.6666666665

Combine like terms: 0.40824829 + 0.6666666665 = 1.0749149565
x = 1.0749149565

Simplifying
x = 1.0749149565

Subproblem 2
x + -0.6666666665 = -0.40824829

Simplifying
x + -0.6666666665 = -0.40824829

Reorder the terms:
-0.6666666665 + x = -0.40824829

Solving
-0.6666666665 + x = -0.40824829

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -0.40824829 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -0.40824829 + 0.6666666665
x = -0.40824829 + 0.6666666665

Combine like terms: -0.40824829 + 0.6666666665 = 0.2584183765
x = 0.2584183765

Simplifying
x = 0.2584183765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0749149565, 0.2584183765}
Solution
x = {1.0749149565, 0.2584183765}