3k^2-6k-72=0

Solution for 3k^2-6k-72=0 equation:

Simplifying
3k2 + -6k + -72 = 0

Reorder the terms:
-72 + -6k + 3k2 = 0

Solving
-72 + -6k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -2k + k2) = 0

Factor a trinomial.
3((-4 + -1k)(6 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve:

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 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 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 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 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-4, 6}