5k^2=-12-19k

Solution for 5k^2=-12-19k equation:

Simplifying
5k2 = -12 + -19k

Solving
5k2 = -12 + -19k

Solving for variable 'k'.

Reorder the terms:
12 + 19k + 5k2 = -12 + -19k + 12 + 19k

Reorder the terms:
12 + 19k + 5k2 = -12 + 12 + -19k + 19k

Combine like terms: -12 + 12 = 0
12 + 19k + 5k2 = 0 + -19k + 19k
12 + 19k + 5k2 = -19k + 19k

Combine like terms: -19k + 19k = 0
12 + 19k + 5k2 = 0

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

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

Simplifying
3 + k = 0

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

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

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

Simplifying
k = -3
Subproblem 2
Set the factor '(4 + 5k)' equal to zero and attempt to solve:

Simplifying
4 + 5k = 0

Solving
4 + 5k = 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 + 5k = 0 + -4

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

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

Divide each side by '5'.
k = -0.8

Simplifying
k = -0.8
Solution
k = {-3, -0.8}