z^2+8z-65=0

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

Simplifying
z2 + 8z + -65 = 0

Reorder the terms:
-65 + 8z + z2 = 0

Solving
-65 + 8z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-13 + -1z = 0

Solving
-13 + -1z = 0

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

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

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

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

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

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

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

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

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

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

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

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