x^2+23x=-120

Solution for x^2+23x=-120 equation:

Simplifying
x2 + 23x = -120

Reorder the terms:
23x + x2 = -120

Solving
23x + x2 = -120

Solving for variable 'x'.

Reorder the terms:
120 + 23x + x2 = -120 + 120

Combine like terms: -120 + 120 = 0
120 + 23x + x2 = 0

Factor a trinomial.
(15 + x)(8 + x) = 0

Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-15, -8}