n^2-2n-96=3

Solution for n^2-2n-96=3 equation:

Simplifying
n2 + -2n + -96 = 3

Reorder the terms:
-96 + -2n + n2 = 3

Solving
-96 + -2n + n2 = 3

Solving for variable 'n'.

Reorder the terms:
-96 + -3 + -2n + n2 = 3 + -3

Combine like terms: -96 + -3 = -99
-99 + -2n + n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-99 + -2n + n2 = 0

Factor a trinomial.
(-9 + -1n)(11 + -1n) = 0

Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-9, 11}