x(x+22)=-120

Solution for x(x+22)=-120 equation:

Simplifying
x(x + 22) = -120

Reorder the terms:
x(22 + x) = -120
(22 * x + x * x) = -120
(22x + x2) = -120

Solving
22x + x2 = -120

Solving for variable 'x'.

Reorder the terms:
120 + 22x + x2 = -120 + 120

Combine like terms: -120 + 120 = 0
120 + 22x + x2 = 0

Factor a trinomial.
(12 + x)(10 + x) = 0

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {-12, -10}