5k^2+23k=-12

Solution for 5k^2+23k=-12 equation:

Simplifying
5k2 + 23k = -12

Reorder the terms:
23k + 5k2 = -12

Solving
23k + 5k2 = -12

Solving for variable 'k'.

Reorder the terms:
12 + 23k + 5k2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 23k + 5k2 = 0

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

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 + 5k)' equal to zero and attempt to solve:

Simplifying
3 + 5k = 0

Solving
3 + 5k = 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 + 5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5k = 0 + -3
5k = 0 + -3

Combine like terms: 0 + -3 = -3
5k = -3

Divide each side by '5'.
k = -0.6

Simplifying
k = -0.6
Solution
k = {-4, -0.6}