-5n^2-3n+54=0

Solution for -5n^2-3n+54=0 equation:

Simplifying
-5n2 + -3n + 54 = 0

Reorder the terms:
54 + -3n + -5n2 = 0

Solving
54 + -3n + -5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -1n)(18 + 5n) = 0

Subproblem 1
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(18 + 5n)' equal to zero and attempt to solve:

Simplifying
18 + 5n = 0

Solving
18 + 5n = 0

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

Add '-18' to each side of the equation.
18 + -18 + 5n = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 5n = 0 + -18
5n = 0 + -18

Combine like terms: 0 + -18 = -18
5n = -18

Divide each side by '5'.
n = -3.6

Simplifying
n = -3.6
Solution
n = {3, -3.6}