4z^3-8z^2=0

Solution for 4z^3-8z^2=0 equation:

Simplifying
4z3 + -8z2 = 0

Reorder the terms:
-8z2 + 4z3 = 0

Solving
-8z2 + 4z3 = 0

Solving for variable 'z'.

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

Ignore the factor 4.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(-2 + z)' equal to zero and attempt to solve:

Simplifying
-2 + z = 0

Solving
-2 + z = 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 + z = 0 + 2

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

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

Simplifying
z = 2
Solution
z = {0, 2}