36x^2-24x+4=6

Solution for 36x^2-24x+4=6 equation:

Simplifying
36x2 + -24x + 4 = 6

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

Solving
4 + -24x + 36x2 = 6

Solving for variable 'x'.

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

Combine like terms: 4 + -6 = -2
-2 + -24x + 36x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-2 + -24x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -12x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -12x + 18x2)' equal to zero and attempt to solve:

Simplifying
-1 + -12x + 18x2 = 0

Solving
-1 + -12x + 18x2 = 0

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

Divide each side by '18'.
-0.05555555556 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.05555555556' to each side of the equation.
-0.05555555556 + -0.6666666667x + 0.05555555556 + x2 = 0 + 0.05555555556

Reorder the terms:
-0.05555555556 + 0.05555555556 + -0.6666666667x + x2 = 0 + 0.05555555556

Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000
0.00000000000 + -0.6666666667x + x2 = 0 + 0.05555555556
-0.6666666667x + x2 = 0 + 0.05555555556

Combine like terms: 0 + 0.05555555556 = 0.05555555556
-0.6666666667x + x2 = 0.05555555556

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 = 0.05555555556 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 0.05555555556 + 0.1111111112

Combine like terms: 0.05555555556 + 0.1111111112 = 0.16666666676
0.1111111112 + -0.6666666667x + x2 = 0.16666666676

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 0.16666666676

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 0.408248291 and -0.408248291.

Subproblem 1
x + -0.3333333334 = 0.408248291

Simplifying
x + -0.3333333334 = 0.408248291

Reorder the terms:
-0.3333333334 + x = 0.408248291

Solving
-0.3333333334 + x = 0.408248291

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 = 0.408248291 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 0.408248291 + 0.3333333334
x = 0.408248291 + 0.3333333334

Combine like terms: 0.408248291 + 0.3333333334 = 0.7415816244
x = 0.7415816244

Simplifying
x = 0.7415816244

Subproblem 2
x + -0.3333333334 = -0.408248291

Simplifying
x + -0.3333333334 = -0.408248291

Reorder the terms:
-0.3333333334 + x = -0.408248291

Solving
-0.3333333334 + x = -0.408248291

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 = -0.408248291 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -0.408248291 + 0.3333333334
x = -0.408248291 + 0.3333333334

Combine like terms: -0.408248291 + 0.3333333334 = -0.0749149576
x = -0.0749149576

Simplifying
x = -0.0749149576

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7415816244, -0.0749149576}
Solution
x = {0.7415816244, -0.0749149576}