54n^2k+300nk-144k=0

Solution for 54n^2k+300nk-144k=0 equation:

Simplifying
54n2k + 300nk + -144k = 0

Reorder the terms:
-144k + 300kn + 54kn2 = 0

Solving
-144k + 300kn + 54kn2 = 0

Solving for variable 'k'.

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

Factor out the Greatest Common Factor (GCF), '6k'.
6k(-24 + 50n + 9n2) = 0

Factor a trinomial.
6k((-6 + -1n)(4 + -9n)) = 0

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

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 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 + -1n = 0 + 6

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

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

Add 'n' to each side of the equation.
-1n + n = 6 + n

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

Simplifying
0 = 6 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(4 + -9n)' equal to zero and attempt to solve:

Simplifying
4 + -9n = 0

Solving
4 + -9n = 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 + -9n = 0 + -4

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

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

Add '9n' to each side of the equation.
-9n + 9n = -4 + 9n

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

Simplifying
0 = -4 + 9n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}