-6k^2+39k-18=0

Solution for -6k^2+39k-18=0 equation:

Simplifying
-6k2 + 39k + -18 = 0

Reorder the terms:
-18 + 39k + -6k2 = 0

Solving
-18 + 39k + -6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 13k + -2k2) = 0

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

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

Simplifying
-6 + k = 0

Solving
-6 + k = 0

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

Add '6' to each side of the equation.
-6 + 6 + k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + k = 0 + 6
k = 0 + 6

Combine like terms: 0 + 6 = 6
k = 6

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

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

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

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {6, 0.5}