12k^2-30k-72=0

Solution for 12k^2-30k-72=0 equation:

Simplifying
12k2 + -30k + -72 = 0

Reorder the terms:
-72 + -30k + 12k2 = 0

Solving
-72 + -30k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -5k + 2k2) = 0

Factor a trinomial.
6((-3 + -2k)(4 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -2k)' equal to zero and attempt to solve:

Simplifying
-3 + -2k = 0

Solving
-3 + -2k = 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 + -2k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2k = 0 + 3
-2k = 0 + 3

Combine like terms: 0 + 3 = 3
-2k = 3

Divide each side by '-2'.
k = -1.5

Simplifying
k = -1.5
Subproblem 2
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
Solution
k = {-1.5, 4}