6n^2x+3nx-18x=0

Solution for 6n^2x+3nx-18x=0 equation:

Simplifying
6n2x + 3nx + -18x = 0

Reorder the terms:
3nx + 6n2x + -18x = 0

Solving
3nx + 6n2x + -18x = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(n + 2n2 + -6) = 0

Factor a trinomial.
3x((2n + -3)(n + 2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2n + -3)' equal to zero and attempt to solve:

Simplifying
2n + -3 = 0

Reorder the terms:
-3 + 2n = 0

Solving
-3 + 2n = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2n = 0 + 3
2n = 0 + 3

Combine like terms: 0 + 3 = 3
2n = 3

Divide each side by '2'.
n = 1.5

Simplifying
n = 1.5
Subproblem 3
Set the factor '(n + 2)' equal to zero and attempt to solve:

Simplifying
n + 2 = 0

Reorder the terms:
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {1.5, -2}