5k^2-21k-54=0

Solution for 5k^2-21k-54=0 equation:

Simplifying
5k2 + -21k + -54 = 0

Reorder the terms:
-54 + -21k + 5k2 = 0

Solving
-54 + -21k + 5k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(-9 + -5k)' equal to zero and attempt to solve:

Simplifying
-9 + -5k = 0

Solving
-9 + -5k = 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 + -5k = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5k = 0 + 9
-5k = 0 + 9

Combine like terms: 0 + 9 = 9
-5k = 9

Divide each side by '-5'.
k = -1.8

Simplifying
k = -1.8
Subproblem 2
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
Solution
k = {-1.8, 6}