(9+x)(12+x)=180

Solution for (9+x)(12+x)=180 equation:

Simplifying
(9 + x)(12 + x) = 180

Multiply (9 + x) * (12 + x)
(9(12 + x) + x(12 + x)) = 180
((12 * 9 + x * 9) + x(12 + x)) = 180
((108 + 9x) + x(12 + x)) = 180
(108 + 9x + (12 * x + x * x)) = 180
(108 + 9x + (12x + x2)) = 180

Combine like terms: 9x + 12x = 21x
(108 + 21x + x2) = 180

Solving
108 + 21x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
108 + -180 + 21x + x2 = 180 + -180

Combine like terms: 108 + -180 = -72
-72 + 21x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-72 + 21x + x2 = 0

Factor a trinomial.
(-24 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-24, 3}