54k^2+564k+240=0

Solution for 54k^2+564k+240=0 equation:

Simplifying
54k2 + 564k + 240 = 0

Reorder the terms:
240 + 564k + 54k2 = 0

Solving
240 + 564k + 54k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(40 + 94k + 9k2) = 0

Factor a trinomial.
6((10 + k)(4 + 9k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(10 + k)' equal to zero and attempt to solve:

Simplifying
10 + k = 0

Solving
10 + k = 0

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

Add '-10' to each side of the equation.
10 + -10 + k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + k = 0 + -10
k = 0 + -10

Combine like terms: 0 + -10 = -10
k = -10

Simplifying
k = -10
Subproblem 2
Set the factor '(4 + 9k)' equal to zero and attempt to solve:

Simplifying
4 + 9k = 0

Solving
4 + 9k = 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 + 9k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9k = 0 + -4
9k = 0 + -4

Combine like terms: 0 + -4 = -4
9k = -4

Divide each side by '9'.
k = -0.4444444444

Simplifying
k = -0.4444444444
Solution
k = {-10, -0.4444444444}