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

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

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

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

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

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

Combine like terms: 2x + 9x = 11x
(6 + 11x + 3x2) = 180

Solving
6 + 11x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
6 + -180 + 11x + 3x2 = 180 + -180

Combine like terms: 6 + -180 = -174
-174 + 11x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-174 + 11x + 3x2 = 0

Factor a trinomial.
(-29 + -3x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-29 + -3x)' equal to zero and attempt to solve:

Simplifying
-29 + -3x = 0

Solving
-29 + -3x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -3x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -3x = 0 + 29
-3x = 0 + 29

Combine like terms: 0 + 29 = 29
-3x = 29

Divide each side by '-3'.
x = -9.666666667

Simplifying
x = -9.666666667
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-9.666666667, 6}