2(3x-2)6x=44

Solution for 2(3x-2)6x=44 equation:

Simplifying
2(3x + -2) * 6x = 44

Reorder the terms:
2(-2 + 3x) * 6x = 44

Reorder the terms for easier multiplication:
2 * 6x(-2 + 3x) = 44

Multiply 2 * 6
12x(-2 + 3x) = 44
(-2 * 12x + 3x * 12x) = 44
(-24x + 36x2) = 44

Solving
-24x + 36x2 = 44

Solving for variable 'x'.

Reorder the terms:
-44 + -24x + 36x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-44 + -24x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + -6x + 9x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-11 + -6x + 9x2)' equal to zero and attempt to solve:

Simplifying
-11 + -6x + 9x2 = 0

Solving
-11 + -6x + 9x2 = 0

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

Divide each side by '9'.
-1.222222222 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + -0.6666666667x + 1.222222222 + x2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + -0.6666666667x + x2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 1.222222222
-0.6666666667x + x2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
-0.6666666667x + x2 = 1.222222222

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 = 1.222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 1.222222222 + 0.1111111112

Combine like terms: 1.222222222 + 0.1111111112 = 1.3333333332
0.1111111112 + -0.6666666667x + x2 = 1.3333333332

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.3333333332

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.154700538 and -1.154700538.

Subproblem 1
x + -0.3333333334 = 1.154700538

Simplifying
x + -0.3333333334 = 1.154700538

Reorder the terms:
-0.3333333334 + x = 1.154700538

Solving
-0.3333333334 + x = 1.154700538

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 = 1.154700538 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.154700538 + 0.3333333334
x = 1.154700538 + 0.3333333334

Combine like terms: 1.154700538 + 0.3333333334 = 1.4880338714
x = 1.4880338714

Simplifying
x = 1.4880338714

Subproblem 2
x + -0.3333333334 = -1.154700538

Simplifying
x + -0.3333333334 = -1.154700538

Reorder the terms:
-0.3333333334 + x = -1.154700538

Solving
-0.3333333334 + x = -1.154700538

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 = -1.154700538 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.154700538 + 0.3333333334
x = -1.154700538 + 0.3333333334

Combine like terms: -1.154700538 + 0.3333333334 = -0.8213672046
x = -0.8213672046

Simplifying
x = -0.8213672046

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4880338714, -0.8213672046}
Solution
x = {1.4880338714, -0.8213672046}