5n^2-6n-144=0

Solution for 5n^2-6n-144=0 equation:

Simplifying
5n2 + -6n + -144 = 0

Reorder the terms:
-144 + -6n + 5n2 = 0

Solving
-144 + -6n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-24 + -5n)(6 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-4.8, 6}