6k^2-54k+120=0

Solution for 6k^2-54k+120=0 equation:

Simplifying
6k2 + -54k + 120 = 0

Reorder the terms:
120 + -54k + 6k2 = 0

Solving
120 + -54k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + -9k + k2) = 0

Factor a trinomial.
6((4 + -1k)(5 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {4, 5}