12k^2+31k+20=0

Solution for 12k^2+31k+20=0 equation:

Simplifying
12k2 + 31k + 20 = 0

Reorder the terms:
20 + 31k + 12k2 = 0

Solving
20 + 31k + 12k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + 3k)(5 + 4k) = 0

Subproblem 1
Set the factor '(4 + 3k)' equal to zero and attempt to solve:

Simplifying
4 + 3k = 0

Solving
4 + 3k = 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 + 3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3k = 0 + -4
3k = 0 + -4

Combine like terms: 0 + -4 = -4
3k = -4

Divide each side by '3'.
k = -1.333333333

Simplifying
k = -1.333333333
Subproblem 2
Set the factor '(5 + 4k)' equal to zero and attempt to solve:

Simplifying
5 + 4k = 0

Solving
5 + 4k = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4k = 0 + -5
4k = 0 + -5

Combine like terms: 0 + -5 = -5
4k = -5

Divide each side by '4'.
k = -1.25

Simplifying
k = -1.25
Solution
k = {-1.333333333, -1.25}