4k^2-2k-12=0

Solution for 4k^2-2k-12=0 equation:

Simplifying
4k2 + -2k + -12 = 0

Reorder the terms:
-12 + -2k + 4k2 = 0

Solving
-12 + -2k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1k + 2k2) = 0

Factor a trinomial.
2((-3 + -2k)(2 + -1k)) = 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 '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

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