3k^2+9=-12k

Solution for 3k^2+9=-12k equation:

Simplifying
3k2 + 9 = -12k

Reorder the terms:
9 + 3k2 = -12k

Solving
9 + 3k2 = -12k

Solving for variable 'k'.

Reorder the terms:
9 + 12k + 3k2 = -12k + 12k

Combine like terms: -12k + 12k = 0
9 + 12k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 4k + k2) = 0

Factor a trinomial.
3((3 + k)(1 + k)) = 0

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

Simplifying
1 + k = 0

Solving
1 + k = 0

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

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

Simplifying
k = -1
Solution
k = {-3, -1}