5n^2-9n-116=0

Solution for 5n^2-9n-116=0 equation:

Simplifying
5n2 + -9n + -116 = 0

Reorder the terms:
-116 + -9n + 5n2 = 0

Solving
-116 + -9n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + -1n)(29 + -5n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

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

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

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

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

Simplifying
n = -4
Subproblem 2
Set the factor '(29 + -5n)' equal to zero and attempt to solve:

Simplifying
29 + -5n = 0

Solving
29 + -5n = 0

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

Add '-29' to each side of the equation.
29 + -29 + -5n = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -5n = 0 + -29
-5n = 0 + -29

Combine like terms: 0 + -29 = -29
-5n = -29

Divide each side by '-5'.
n = 5.8

Simplifying
n = 5.8
Solution
n = {-4, 5.8}