k^2+22k+120=0

Solution for k^2+22k+120=0 equation:

Simplifying
k2 + 22k + 120 = 0

Reorder the terms:
120 + 22k + k2 = 0

Solving
120 + 22k + k2 = 0

Solving for variable 'k'.

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

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

Simplifying
12 + k = 0

Solving
12 + k = 0

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

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

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

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

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

Simplifying
10 + k = 0

Solving
10 + k = 0

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

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

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

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

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