3x(4x+2)-4(6-2x)=2(9-x)

Solution for 3x(4x+2)-4(6-2x)=2(9-x) equation:

Simplifying
3x(4x + 2) + -4(6 + -2x) = 2(9 + -1x)

Reorder the terms:
3x(2 + 4x) + -4(6 + -2x) = 2(9 + -1x)
(2 * 3x + 4x * 3x) + -4(6 + -2x) = 2(9 + -1x)
(6x + 12x2) + -4(6 + -2x) = 2(9 + -1x)
6x + 12x2 + (6 * -4 + -2x * -4) = 2(9 + -1x)
6x + 12x2 + (-24 + 8x) = 2(9 + -1x)

Reorder the terms:
-24 + 6x + 8x + 12x2 = 2(9 + -1x)

Combine like terms: 6x + 8x = 14x
-24 + 14x + 12x2 = 2(9 + -1x)
-24 + 14x + 12x2 = (9 * 2 + -1x * 2)
-24 + 14x + 12x2 = (18 + -2x)

Solving
-24 + 14x + 12x2 = 18 + -2x

Solving for variable 'x'.

Reorder the terms:
-24 + -18 + 14x + 2x + 12x2 = 18 + -2x + -18 + 2x

Combine like terms: -24 + -18 = -42
-42 + 14x + 2x + 12x2 = 18 + -2x + -18 + 2x

Combine like terms: 14x + 2x = 16x
-42 + 16x + 12x2 = 18 + -2x + -18 + 2x

Reorder the terms:
-42 + 16x + 12x2 = 18 + -18 + -2x + 2x

Combine like terms: 18 + -18 = 0
-42 + 16x + 12x2 = 0 + -2x + 2x
-42 + 16x + 12x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-42 + 16x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 8x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 8x + 6x2)' equal to zero and attempt to solve:

Simplifying
-21 + 8x + 6x2 = 0

Solving
-21 + 8x + 6x2 = 0

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

Divide each side by '6'.
-3.5 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 1.333333333x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 1.333333333x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 1.333333333x + x2 = 0 + 3.5
1.333333333x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
1.333333333x + x2 = 3.5

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 = 3.5 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 3.5 + 0.4444444442

Combine like terms: 3.5 + 0.4444444442 = 3.9444444442
0.4444444442 + 1.333333333x + x2 = 3.9444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 3.9444444442

Calculate the square root of the right side: 1.986062548

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.986062548 and -1.986062548.

Subproblem 1
x + 0.6666666665 = 1.986062548

Simplifying
x + 0.6666666665 = 1.986062548

Reorder the terms:
0.6666666665 + x = 1.986062548

Solving
0.6666666665 + x = 1.986062548

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 = 1.986062548 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.986062548 + -0.6666666665
x = 1.986062548 + -0.6666666665

Combine like terms: 1.986062548 + -0.6666666665 = 1.3193958815
x = 1.3193958815

Simplifying
x = 1.3193958815

Subproblem 2
x + 0.6666666665 = -1.986062548

Simplifying
x + 0.6666666665 = -1.986062548

Reorder the terms:
0.6666666665 + x = -1.986062548

Solving
0.6666666665 + x = -1.986062548

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 = -1.986062548 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.986062548 + -0.6666666665
x = -1.986062548 + -0.6666666665

Combine like terms: -1.986062548 + -0.6666666665 = -2.6527292145
x = -2.6527292145

Simplifying
x = -2.6527292145

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3193958815, -2.6527292145}
Solution
x = {1.3193958815, -2.6527292145}