n^2=10n+96

Solution for n^2=10n+96 equation:

Simplifying
n2 = 10n + 96

Reorder the terms:
n2 = 96 + 10n

Solving
n2 = 96 + 10n

Solving for variable 'n'.

Reorder the terms:
-96 + -10n + n2 = 96 + 10n + -96 + -10n

Reorder the terms:
-96 + -10n + n2 = 96 + -96 + 10n + -10n

Combine like terms: 96 + -96 = 0
-96 + -10n + n2 = 0 + 10n + -10n
-96 + -10n + n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-96 + -10n + n2 = 0

Factor a trinomial.
(-6 + -1n)(16 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Solution
n = {-6, 16}