-5n^2-2n+72=0

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

Simplifying
-5n2 + -2n + 72 = 0

Reorder the terms:
72 + -2n + -5n2 = 0

Solving
72 + -2n + -5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(18 + -5n)(4 + n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 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 + n = 0 + -4

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

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

Simplifying
n = -4
Solution
n = {3.6, -4}