12k^2+2k-24=0

Solution for 12k^2+2k-24=0 equation:

Simplifying
12k2 + 2k + -24 = 0

Reorder the terms:
-24 + 2k + 12k2 = 0

Solving
-24 + 2k + 12k2 = 0

Solving for variable 'k'.

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

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

Ignore the factor 2.
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 + -3k)' equal to zero and attempt to solve:

Simplifying
4 + -3k = 0

Solving
4 + -3k = 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 + -3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3k = 0 + -4
-3k = 0 + -4

Combine like terms: 0 + -4 = -4
-3k = -4

Divide each side by '-3'.
k = 1.333333333

Simplifying
k = 1.333333333
Solution
k = {-1.5, 1.333333333}