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

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

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

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

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

Multiply (2 + 3x) * (3 + 2x)
(2(3 + 2x) + 3x * (3 + 2x)) = 180
((3 * 2 + 2x * 2) + 3x * (3 + 2x)) = 180
((6 + 4x) + 3x * (3 + 2x)) = 180
(6 + 4x + (3 * 3x + 2x * 3x)) = 180
(6 + 4x + (9x + 6x2)) = 180

Combine like terms: 4x + 9x = 13x
(6 + 13x + 6x2) = 180

Solving
6 + 13x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
6 + -180 + 13x + 6x2 = 180 + -180

Combine like terms: 6 + -180 = -174
-174 + 13x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-174 + 13x + 6x2 = 0

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

Divide each side by '6'.
-29 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 2.166666667x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 2.166666667x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 2.166666667x + x2 = 0 + 29
2.166666667x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
2.166666667x + x2 = 29

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 29 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 29 + 1.173611113

Combine like terms: 29 + 1.173611113 = 30.173611113
1.173611113 + 2.166666667x + x2 = 30.173611113

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 30.173611113

Calculate the square root of the right side: 5.493051166

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 5.493051166 and -5.493051166.

Subproblem 1
x + 1.083333334 = 5.493051166

Simplifying
x + 1.083333334 = 5.493051166

Reorder the terms:
1.083333334 + x = 5.493051166

Solving
1.083333334 + x = 5.493051166

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = 5.493051166 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 5.493051166 + -1.083333334
x = 5.493051166 + -1.083333334

Combine like terms: 5.493051166 + -1.083333334 = 4.409717832
x = 4.409717832

Simplifying
x = 4.409717832

Subproblem 2
x + 1.083333334 = -5.493051166

Simplifying
x + 1.083333334 = -5.493051166

Reorder the terms:
1.083333334 + x = -5.493051166

Solving
1.083333334 + x = -5.493051166

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = -5.493051166 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -5.493051166 + -1.083333334
x = -5.493051166 + -1.083333334

Combine like terms: -5.493051166 + -1.083333334 = -6.5763845
x = -6.5763845

Simplifying
x = -6.5763845

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.409717832, -6.5763845}