6*K^2-K-12=0

Solution for 6*K^2-K-12=0 equation:

Simplifying
6K2 + -1K + -12 = 0

Reorder the terms:
-12 + -1K + 6K2 = 0

Solving
-12 + -1K + 6K2 = 0

Solving for variable 'K'.

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

Subproblem 1
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
Subproblem 2
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
Solution
K = {-1.333333333, 1.5}