6k^2+3k-18=0

Solution for 6k^2+3k-18=0 equation:

Simplifying
6k2 + 3k + -18 = 0

Reorder the terms:
-18 + 3k + 6k2 = 0

Solving
-18 + 3k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + k + 2k2) = 0

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

Ignore the factor 3.
Subproblem 1
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
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 = {-2, 1.5}