(3x+2)(2x+180)=90

Solution for (3x+2)(2x+180)=90 equation:

Simplifying
(3x + 2)(2x + 180) = 90

Reorder the terms:
(2 + 3x)(2x + 180) = 90

Reorder the terms:
(2 + 3x)(180 + 2x) = 90

Multiply (2 + 3x) * (180 + 2x)
(2(180 + 2x) + 3x * (180 + 2x)) = 90
((180 * 2 + 2x * 2) + 3x * (180 + 2x)) = 90
((360 + 4x) + 3x * (180 + 2x)) = 90
(360 + 4x + (180 * 3x + 2x * 3x)) = 90
(360 + 4x + (540x + 6x2)) = 90

Combine like terms: 4x + 540x = 544x
(360 + 544x + 6x2) = 90

Solving
360 + 544x + 6x2 = 90

Solving for variable 'x'.

Reorder the terms:
360 + -90 + 544x + 6x2 = 90 + -90

Combine like terms: 360 + -90 = 270
270 + 544x + 6x2 = 90 + -90

Combine like terms: 90 + -90 = 0
270 + 544x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(135 + 272x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(135 + 272x + 3x2)' equal to zero and attempt to solve:

Simplifying
135 + 272x + 3x2 = 0

Solving
135 + 272x + 3x2 = 0

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

Divide each side by '3'.
45 + 90.66666667x + x2 = 0

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 90.66666667x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + 90.66666667x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 90.66666667x + x2 = 0 + -45
90.66666667x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
90.66666667x + x2 = -45

The x term is 90.66666667x.  Take half its coefficient (45.33333334).
Square it (2055.111112) and add it to both sides.

Add '2055.111112' to each side of the equation.
90.66666667x + 2055.111112 + x2 = -45 + 2055.111112

Reorder the terms:
2055.111112 + 90.66666667x + x2 = -45 + 2055.111112

Combine like terms: -45 + 2055.111112 = 2010.111112
2055.111112 + 90.66666667x + x2 = 2010.111112

Factor a perfect square on the left side:
(x + 45.33333334)(x + 45.33333334) = 2010.111112

Calculate the square root of the right side: 44.834262702

Break this problem into two subproblems by setting 
(x + 45.33333334) equal to 44.834262702 and -44.834262702.

Subproblem 1
x + 45.33333334 = 44.834262702

Simplifying
x + 45.33333334 = 44.834262702

Reorder the terms:
45.33333334 + x = 44.834262702

Solving
45.33333334 + x = 44.834262702

Solving for variable 'x'.

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

Add '-45.33333334' to each side of the equation.
45.33333334 + -45.33333334 + x = 44.834262702 + -45.33333334

Combine like terms: 45.33333334 + -45.33333334 = 0.00000000
0.00000000 + x = 44.834262702 + -45.33333334
x = 44.834262702 + -45.33333334

Combine like terms: 44.834262702 + -45.33333334 = -0.499070638
x = -0.499070638

Simplifying
x = -0.499070638

Subproblem 2
x + 45.33333334 = -44.834262702

Simplifying
x + 45.33333334 = -44.834262702

Reorder the terms:
45.33333334 + x = -44.834262702

Solving
45.33333334 + x = -44.834262702

Solving for variable 'x'.

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

Add '-45.33333334' to each side of the equation.
45.33333334 + -45.33333334 + x = -44.834262702 + -45.33333334

Combine like terms: 45.33333334 + -45.33333334 = 0.00000000
0.00000000 + x = -44.834262702 + -45.33333334
x = -44.834262702 + -45.33333334

Combine like terms: -44.834262702 + -45.33333334 = -90.167596042
x = -90.167596042

Simplifying
x = -90.167596042

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.499070638, -90.167596042}
Solution
x = {-0.499070638, -90.167596042}