8z^2-6z-5=0

Solution for 8z^2-6z-5=0 equation:

Simplifying
8z2 + -6z + -5 = 0

Reorder the terms:
-5 + -6z + 8z2 = 0

Solving
-5 + -6z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -2z)(5 + -4z) = 0

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

Simplifying
-1 + -2z = 0

Solving
-1 + -2z = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2z = 0 + 1
-2z = 0 + 1

Combine like terms: 0 + 1 = 1
-2z = 1

Divide each side by '-2'.
z = -0.5

Simplifying
z = -0.5
Subproblem 2
Set the factor '(5 + -4z)' equal to zero and attempt to solve:

Simplifying
5 + -4z = 0

Solving
5 + -4z = 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 + -4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z = 0 + -5
-4z = 0 + -5

Combine like terms: 0 + -5 = -5
-4z = -5

Divide each side by '-4'.
z = 1.25

Simplifying
z = 1.25
Solution
z = {-0.5, 1.25}