5k^2+180=-60k

Solution for 5k^2+180=-60k equation:

Simplifying
5k2 + 180 = -60k

Reorder the terms:
180 + 5k2 = -60k

Solving
180 + 5k2 = -60k

Solving for variable 'k'.

Reorder the terms:
180 + 60k + 5k2 = -60k + 60k

Combine like terms: -60k + 60k = 0
180 + 60k + 5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + 12k + k2) = 0

Factor a trinomial.
5((6 + k)(6 + k)) = 0

Ignore the factor 5.
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 '(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 = {-6, -6}