5n^2-9n-80=0

Solution for 5n^2-9n-80=0 equation:

Simplifying
5n2 + -9n + -80 = 0

Reorder the terms:
-80 + -9n + 5n2 = 0

Solving
-80 + -9n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-16 + -5n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-16 + -5n)' equal to zero and attempt to solve:

Simplifying
-16 + -5n = 0

Solving
-16 + -5n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5n = 0 + 16
-5n = 0 + 16

Combine like terms: 0 + 16 = 16
-5n = 16

Divide each side by '-5'.
n = -3.2

Simplifying
n = -3.2
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-3.2, 5}