3(3x+4)2x=4

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

Simplifying
3(3x + 4) * 2x = 4

Reorder the terms:
3(4 + 3x) * 2x = 4

Reorder the terms for easier multiplication:
3 * 2x(4 + 3x) = 4

Multiply 3 * 2
6x(4 + 3x) = 4
(4 * 6x + 3x * 6x) = 4
(24x + 18x2) = 4

Solving
24x + 18x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 24x + 18x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 24x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 12x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 12x + 9x2)' equal to zero and attempt to solve:

Simplifying
-2 + 12x + 9x2 = 0

Solving
-2 + 12x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 1.333333333x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + 1.333333333x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + 1.333333333x + x2 = 0 + 0.2222222222
1.333333333x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
1.333333333x + x2 = 0.2222222222

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 = 0.2222222222 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 0.2222222222 + 0.4444444442

Combine like terms: 0.2222222222 + 0.4444444442 = 0.6666666664
0.4444444442 + 1.333333333x + x2 = 0.6666666664

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 0.6666666664

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 0.816496581 and -0.816496581.

Subproblem 1
x + 0.6666666665 = 0.816496581

Simplifying
x + 0.6666666665 = 0.816496581

Reorder the terms:
0.6666666665 + x = 0.816496581

Solving
0.6666666665 + x = 0.816496581

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 = 0.816496581 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 0.816496581 + -0.6666666665
x = 0.816496581 + -0.6666666665

Combine like terms: 0.816496581 + -0.6666666665 = 0.1498299145
x = 0.1498299145

Simplifying
x = 0.1498299145

Subproblem 2
x + 0.6666666665 = -0.816496581

Simplifying
x + 0.6666666665 = -0.816496581

Reorder the terms:
0.6666666665 + x = -0.816496581

Solving
0.6666666665 + x = -0.816496581

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 = -0.816496581 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -0.816496581 + -0.6666666665
x = -0.816496581 + -0.6666666665

Combine like terms: -0.816496581 + -0.6666666665 = -1.4831632475
x = -1.4831632475

Simplifying
x = -1.4831632475

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1498299145, -1.4831632475}
Solution
x = {0.1498299145, -1.4831632475}