5k^2-15k-270=0

Solution for 5k^2-15k-270=0 equation:

Simplifying
5k2 + -15k + -270 = 0

Reorder the terms:
-270 + -15k + 5k2 = 0

Solving
-270 + -15k + 5k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-54 + -3k + k2) = 0

Factor a trinomial.
5((-6 + -1k)(9 + -1k)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 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 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(9 + -1k)' equal to zero and attempt to solve:

Simplifying
9 + -1k = 0

Solving
9 + -1k = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1k = 0 + -9
-1k = 0 + -9

Combine like terms: 0 + -9 = -9
-1k = -9

Divide each side by '-1'.
k = 9

Simplifying
k = 9
Solution
k = {-6, 9}