s^2-8s-65=0

Solution for s^2-8s-65=0 equation:

Simplifying
s2 + -8s + -65 = 0

Reorder the terms:
-65 + -8s + s2 = 0

Solving
-65 + -8s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-5 + -1s)(13 + -1s) = 0

Subproblem 1
Set the factor '(-5 + -1s)' equal to zero and attempt to solve:

Simplifying
-5 + -1s = 0

Solving
-5 + -1s = 0

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

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

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

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

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

Simplifying
s = -5
Subproblem 2
Set the factor '(13 + -1s)' equal to zero and attempt to solve:

Simplifying
13 + -1s = 0

Solving
13 + -1s = 0

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

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

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

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

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

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