-n^2+14n+72=0

Solution for -n^2+14n+72=0 equation:

Simplifying
-1n2 + 14n + 72 = 0

Reorder the terms:
72 + 14n + -1n2 = 0

Solving
72 + 14n + -1n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(18 + -1n)(4 + n) = 0

Subproblem 1
Set the factor '(18 + -1n)' equal to zero and attempt to solve:

Simplifying
18 + -1n = 0

Solving
18 + -1n = 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 + -1n = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1n = 0 + -18
-1n = 0 + -18

Combine like terms: 0 + -18 = -18
-1n = -18

Divide each side by '-1'.
n = 18

Simplifying
n = 18
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 = {18, -4}