4z^3-4z-8z=0

Solution for 4z^3-4z-8z=0 equation:

Simplifying
4z3 + -4z + -8z = 0

Reorder the terms:
-4z + -8z + 4z3 = 0

Combine like terms: -4z + -8z = -12z
-12z + 4z3 = 0

Solving
-12z + 4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-3 + z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-3 + z2)' equal to zero and attempt to solve:

Simplifying
-3 + z2 = 0

Solving
-3 + z2 = 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 + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + z2 = 0 + 3
z2 = 0 + 3

Combine like terms: 0 + 3 = 3
z2 = 3

Simplifying
z2 = 3

Take the square root of each side:
z = {-1.732050808, 1.732050808}
Solution
z = {0, -1.732050808, 1.732050808}