18k^2-9k-27=0

Solution for 18k^2-9k-27=0 equation:

Simplifying
18k2 + -9k + -27 = 0

Reorder the terms:
-27 + -9k + 18k2 = 0

Solving
-27 + -9k + 18k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + -1k + 2k2) = 0

Factor a trinomial.
9((-1 + -1k)(3 + -2k)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve:

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 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 + -1k = 0 + 1

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

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

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

Simplifying
k = -1
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, 1.5}