8z^2+2z-3=0

Solution for 8z^2+2z-3=0 equation:

Simplifying
8z2 + 2z + -3 = 0

Reorder the terms:
-3 + 2z + 8z2 = 0

Solving
-3 + 2z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -4z)(1 + -2z) = 0

Subproblem 1
Set the factor '(-3 + -4z)' equal to zero and attempt to solve:

Simplifying
-3 + -4z = 0

Solving
-3 + -4z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4z = 0 + 3
-4z = 0 + 3

Combine like terms: 0 + 3 = 3
-4z = 3

Divide each side by '-4'.
z = -0.75

Simplifying
z = -0.75
Subproblem 2
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
Solution
z = {-0.75, 0.5}