-2z^3(6z^2-5z-4)=0

Solution for -2z^3(6z^2-5z-4)=0 equation:

Simplifying
-2z3(6z2 + -5z + -4) = 0

Reorder the terms:
-2z3(-4 + -5z + 6z2) = 0
(-4 * -2z3 + -5z * -2z3 + 6z2 * -2z3) = 0
(8z3 + 10z4 + -12z5) = 0

Solving
8z3 + 10z4 + -12z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z3'.
2z3(4 + 5z + -6z2) = 0

Factor a trinomial.
2z3((4 + -3z)(1 + 2z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve:

Simplifying
z3 = 0

Solving
z3 = 0

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

Simplifying
z3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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 3
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 = {1.333333333, -0.5}