3z^2-2z-8=0

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

Simplifying
3z2 + -2z + -8 = 0

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

Solving
-8 + -2z + 3z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-4 + -3z = 0

Solving
-4 + -3z = 0

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

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

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

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

Divide each side by '-3'.
z = -1.333333333

Simplifying
z = -1.333333333
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-1.333333333, 2}