3k^2+27k=-60

Solution for 3k^2+27k=-60 equation:

Simplifying
3k2 + 27k = -60

Reorder the terms:
27k + 3k2 = -60

Solving
27k + 3k2 = -60

Solving for variable 'k'.

Reorder the terms:
60 + 27k + 3k2 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + 27k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + 9k + k2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve:

Simplifying
5 + k = 0

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

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

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

Simplifying
k = -5
Subproblem 2
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
Solution
k = {-5, -4}