(4x+2)(3x+4)=180

Solution for (4x+2)(3x+4)=180 equation:

Simplifying
(4x + 2)(3x + 4) = 180

Reorder the terms:
(2 + 4x)(3x + 4) = 180

Reorder the terms:
(2 + 4x)(4 + 3x) = 180

Multiply (2 + 4x) * (4 + 3x)
(2(4 + 3x) + 4x * (4 + 3x)) = 180
((4 * 2 + 3x * 2) + 4x * (4 + 3x)) = 180
((8 + 6x) + 4x * (4 + 3x)) = 180
(8 + 6x + (4 * 4x + 3x * 4x)) = 180
(8 + 6x + (16x + 12x2)) = 180

Combine like terms: 6x + 16x = 22x
(8 + 22x + 12x2) = 180

Solving
8 + 22x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
8 + -180 + 22x + 12x2 = 180 + -180

Combine like terms: 8 + -180 = -172
-172 + 22x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-172 + 22x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-86 + 11x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-86 + 11x + 6x2)' equal to zero and attempt to solve:

Simplifying
-86 + 11x + 6x2 = 0

Solving
-86 + 11x + 6x2 = 0

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

Divide each side by '6'.
-14.33333333 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '14.33333333' to each side of the equation.
-14.33333333 + 1.833333333x + 14.33333333 + x2 = 0 + 14.33333333

Reorder the terms:
-14.33333333 + 14.33333333 + 1.833333333x + x2 = 0 + 14.33333333

Combine like terms: -14.33333333 + 14.33333333 = 0.00000000
0.00000000 + 1.833333333x + x2 = 0 + 14.33333333
1.833333333x + x2 = 0 + 14.33333333

Combine like terms: 0 + 14.33333333 = 14.33333333
1.833333333x + x2 = 14.33333333

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 14.33333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 14.33333333 + 0.8402777775

Combine like terms: 14.33333333 + 0.8402777775 = 15.1736111075
0.8402777775 + 1.833333333x + x2 = 15.1736111075

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 15.1736111075

Calculate the square root of the right side: 3.895331964

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 3.895331964 and -3.895331964.

Subproblem 1
x + 0.9166666665 = 3.895331964

Simplifying
x + 0.9166666665 = 3.895331964

Reorder the terms:
0.9166666665 + x = 3.895331964

Solving
0.9166666665 + x = 3.895331964

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 3.895331964 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 3.895331964 + -0.9166666665
x = 3.895331964 + -0.9166666665

Combine like terms: 3.895331964 + -0.9166666665 = 2.9786652975
x = 2.9786652975

Simplifying
x = 2.9786652975

Subproblem 2
x + 0.9166666665 = -3.895331964

Simplifying
x + 0.9166666665 = -3.895331964

Reorder the terms:
0.9166666665 + x = -3.895331964

Solving
0.9166666665 + x = -3.895331964

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -3.895331964 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -3.895331964 + -0.9166666665
x = -3.895331964 + -0.9166666665

Combine like terms: -3.895331964 + -0.9166666665 = -4.8119986305
x = -4.8119986305

Simplifying
x = -4.8119986305

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.9786652975, -4.8119986305}
Solution
x = {2.9786652975, -4.8119986305}