n^2+4n-5=91

Solution for n^2+4n-5=91 equation:

Simplifying
n2 + 4n + -5 = 91

Reorder the terms:
-5 + 4n + n2 = 91

Solving
-5 + 4n + n2 = 91

Solving for variable 'n'.

Reorder the terms:
-5 + -91 + 4n + n2 = 91 + -91

Combine like terms: -5 + -91 = -96
-96 + 4n + n2 = 91 + -91

Combine like terms: 91 + -91 = 0
-96 + 4n + n2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-12, 8}