5n^2-9n-72=0

Solution for 5n^2-9n-72=0 equation:

Simplifying
5n2 + -9n + -72 = 0

Reorder the terms:
-72 + -9n + 5n2 = 0

Solving
-72 + -9n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(24 + -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 '(24 + -5n)' equal to zero and attempt to solve:

Simplifying
24 + -5n = 0

Solving
24 + -5n = 0

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

Add '-24' to each side of the equation.
24 + -24 + -5n = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -5n = 0 + -24
-5n = 0 + -24

Combine like terms: 0 + -24 = -24
-5n = -24

Divide each side by '-5'.
n = 4.8

Simplifying
n = 4.8
Solution
n = {-3, 4.8}