(x+9)(x+2)=120

Solution for (x+9)(x+2)=120 equation:

Simplifying
(x + 9)(x + 2) = 120

Reorder the terms:
(9 + x)(x + 2) = 120

Reorder the terms:
(9 + x)(2 + x) = 120

Multiply (9 + x) * (2 + x)
(9(2 + x) + x(2 + x)) = 120
((2 * 9 + x * 9) + x(2 + x)) = 120
((18 + 9x) + x(2 + x)) = 120
(18 + 9x + (2 * x + x * x)) = 120
(18 + 9x + (2x + x2)) = 120

Combine like terms: 9x + 2x = 11x
(18 + 11x + x2) = 120

Solving
18 + 11x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
18 + -120 + 11x + x2 = 120 + -120

Combine like terms: 18 + -120 = -102
-102 + 11x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-102 + 11x + x2 = 0

Factor a trinomial.
(-17 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
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 = {-17, 6}