20k^2+110k+120=0

Solution for 20k^2+110k+120=0 equation:

Simplifying
20k2 + 110k + 120 = 0

Reorder the terms:
120 + 110k + 20k2 = 0

Solving
120 + 110k + 20k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '10'.
10(12 + 11k + 2k2) = 0

Factor a trinomial.
10((4 + k)(3 + 2k)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(4 + k)' equal to zero and attempt to solve:

Simplifying
4 + k = 0

Solving
4 + k = 0

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

Add '-4' to each side of the equation.
4 + -4 + k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + k = 0 + -4
k = 0 + -4

Combine like terms: 0 + -4 = -4
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Solution
k = {-4, -1.5}