3k^2=-12-20k

Solution for 3k^2=-12-20k equation:

Simplifying
3k2 = -12 + -20k

Solving
3k2 = -12 + -20k

Solving for variable 'k'.

Reorder the terms:
12 + 20k + 3k2 = -12 + -20k + 12 + 20k

Reorder the terms:
12 + 20k + 3k2 = -12 + 12 + -20k + 20k

Combine like terms: -12 + 12 = 0
12 + 20k + 3k2 = 0 + -20k + 20k
12 + 20k + 3k2 = -20k + 20k

Combine like terms: -20k + 20k = 0
12 + 20k + 3k2 = 0

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

Subproblem 1
Set the factor '(6 + k)' equal to zero and attempt to solve:

Simplifying
6 + k = 0

Solving
6 + k = 0

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

Add '-6' to each side of the equation.
6 + -6 + k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + k = 0 + -6
k = 0 + -6

Combine like terms: 0 + -6 = -6
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(2 + 3k)' equal to zero and attempt to solve:

Simplifying
2 + 3k = 0

Solving
2 + 3k = 0

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

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

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

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

Divide each side by '3'.
k = -0.6666666667

Simplifying
k = -0.6666666667
Solution
k = {-6, -0.6666666667}