n^2+8n-65=0

Solution for n^2+8n-65=0 equation:

Simplifying
n2 + 8n + -65 = 0

Reorder the terms:
-65 + 8n + n2 = 0

Solving
-65 + 8n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-13 + -1n)(5 + -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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-13, 5}