0=4n+96-n^2

Solution for 0=4n+96-n^2 equation:

Simplifying
0 = 4n + 96 + -1n2

Reorder the terms:
0 = 96 + 4n + -1n2

Solving
0 = 96 + 4n + -1n2

Solving for variable 'n'.

Combine like terms: 0 + -96 = -96
-96 + -4n + n2 = 96 + 4n + -1n2 + -96 + -4n + n2

Reorder the terms:
-96 + -4n + n2 = 96 + -96 + 4n + -4n + -1n2 + n2

Combine like terms: 96 + -96 = 0
-96 + -4n + n2 = 0 + 4n + -4n + -1n2 + n2
-96 + -4n + n2 = 4n + -4n + -1n2 + n2

Combine like terms: 4n + -4n = 0
-96 + -4n + n2 = 0 + -1n2 + n2
-96 + -4n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-96 + -4n + n2 = 0

Factor a trinomial.
(-8 + -1n)(12 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-8, 12}