3k^2+72=-33k

Solution for 3k^2+72=-33k equation:

Simplifying
3k2 + 72 = -33k

Reorder the terms:
72 + 3k2 = -33k

Solving
72 + 3k2 = -33k

Solving for variable 'k'.

Reorder the terms:
72 + 33k + 3k2 = -33k + 33k

Combine like terms: -33k + 33k = 0
72 + 33k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 11k + k2) = 0

Factor a trinomial.
3((8 + k)(3 + k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + k)' equal to zero and attempt to solve:

Simplifying
8 + k = 0

Solving
8 + k = 0

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

Add '-8' to each side of the equation.
8 + -8 + k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + k = 0 + -8
k = 0 + -8

Combine like terms: 0 + -8 = -8
k = -8

Simplifying
k = -8
Subproblem 2
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
Solution
k = {-8, -3}