n^2+6n-86=5

Solution for n^2+6n-86=5 equation:

Simplifying
n2 + 6n + -86 = 5

Reorder the terms:
-86 + 6n + n2 = 5

Solving
-86 + 6n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
-86 + -5 + 6n + n2 = 5 + -5

Combine like terms: -86 + -5 = -91
-91 + 6n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-91 + 6n + n2 = 0

Factor a trinomial.
(-13 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -1n)' equal to zero and attempt to solve:

Simplifying
-13 + -1n = 0

Solving
-13 + -1n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1n = 0 + 13
-1n = 0 + 13

Combine like terms: 0 + 13 = 13
-1n = 13

Divide each side by '-1'.
n = -13

Simplifying
n = -13
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-13, 7}