4k^2+60k+216=0

Solution for 4k^2+60k+216=0 equation:

Simplifying
4k2 + 60k + 216 = 0

Reorder the terms:
216 + 60k + 4k2 = 0

Solving
216 + 60k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(54 + 15k + k2) = 0

Factor a trinomial.
4((9 + k)(6 + k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(9 + k)' equal to zero and attempt to solve:

Simplifying
9 + k = 0

Solving
9 + k = 0

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

Add '-9' to each side of the equation.
9 + -9 + k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + k = 0 + -9
k = 0 + -9

Combine like terms: 0 + -9 = -9
k = -9

Simplifying
k = -9
Subproblem 2
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
Solution
k = {-9, -6}