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

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

Simplifying
2(6x + 4)(3x + 2) = 2

Reorder the terms:
2(4 + 6x)(3x + 2) = 2

Reorder the terms:
2(4 + 6x)(2 + 3x) = 2

Multiply (4 + 6x) * (2 + 3x)
2(4(2 + 3x) + 6x * (2 + 3x)) = 2
2((2 * 4 + 3x * 4) + 6x * (2 + 3x)) = 2
2((8 + 12x) + 6x * (2 + 3x)) = 2
2(8 + 12x + (2 * 6x + 3x * 6x)) = 2
2(8 + 12x + (12x + 18x2)) = 2

Combine like terms: 12x + 12x = 24x
2(8 + 24x + 18x2) = 2
(8 * 2 + 24x * 2 + 18x2 * 2) = 2
(16 + 48x + 36x2) = 2

Solving
16 + 48x + 36x2 = 2

Solving for variable 'x'.

Reorder the terms:
16 + -2 + 48x + 36x2 = 2 + -2

Combine like terms: 16 + -2 = 14
14 + 48x + 36x2 = 2 + -2

Combine like terms: 2 + -2 = 0
14 + 48x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 24x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 24x + 18x2)' equal to zero and attempt to solve:

Simplifying
7 + 24x + 18x2 = 0

Solving
7 + 24x + 18x2 = 0

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

Divide each side by '18'.
0.3888888889 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.3888888889' to each side of the equation.
0.3888888889 + 1.333333333x + -0.3888888889 + x2 = 0 + -0.3888888889

Reorder the terms:
0.3888888889 + -0.3888888889 + 1.333333333x + x2 = 0 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + 1.333333333x + x2 = 0 + -0.3888888889
1.333333333x + x2 = 0 + -0.3888888889

Combine like terms: 0 + -0.3888888889 = -0.3888888889
1.333333333x + x2 = -0.3888888889

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 = -0.3888888889 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = -0.3888888889 + 0.4444444442

Combine like terms: -0.3888888889 + 0.4444444442 = 0.0555555553
0.4444444442 + 1.333333333x + x2 = 0.0555555553

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 0.0555555553

Calculate the square root of the right side: 0.23570226

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 0.23570226 and -0.23570226.

Subproblem 1
x + 0.6666666665 = 0.23570226

Simplifying
x + 0.6666666665 = 0.23570226

Reorder the terms:
0.6666666665 + x = 0.23570226

Solving
0.6666666665 + x = 0.23570226

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 = 0.23570226 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 0.23570226 + -0.6666666665
x = 0.23570226 + -0.6666666665

Combine like terms: 0.23570226 + -0.6666666665 = -0.4309644065
x = -0.4309644065

Simplifying
x = -0.4309644065

Subproblem 2
x + 0.6666666665 = -0.23570226

Simplifying
x + 0.6666666665 = -0.23570226

Reorder the terms:
0.6666666665 + x = -0.23570226

Solving
0.6666666665 + x = -0.23570226

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 = -0.23570226 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -0.23570226 + -0.6666666665
x = -0.23570226 + -0.6666666665

Combine like terms: -0.23570226 + -0.6666666665 = -0.9023689265
x = -0.9023689265

Simplifying
x = -0.9023689265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.4309644065, -0.9023689265}
Solution
x = {-0.4309644065, -0.9023689265}