a^2+8a-65=0

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

Simplifying
a2 + 8a + -65 = 0

Reorder the terms:
-65 + 8a + a2 = 0

Solving
-65 + 8a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-13 + -1a = 0

Solving
-13 + -1a = 0

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

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

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

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

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

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

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

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

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

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

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

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