5z^3-500z=0

Solution for 5z^3-500z=0 equation:

Simplifying
5z3 + -500z = 0

Reorder the terms:
-500z + 5z3 = 0

Solving
-500z + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(-100 + z2) = 0

Factor a difference between two squares.
5z((10 + z)(-10 + z)) = 0

Ignore the factor 5.
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 '(10 + z)' equal to zero and attempt to solve:

Simplifying
10 + z = 0

Solving
10 + z = 0

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

Add '-10' to each side of the equation.
10 + -10 + z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + z = 0 + -10
z = 0 + -10

Combine like terms: 0 + -10 = -10
z = -10

Simplifying
z = -10
Subproblem 3
Set the factor '(-10 + z)' equal to zero and attempt to solve:

Simplifying
-10 + z = 0

Solving
-10 + z = 0

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

Add '10' to each side of the equation.
-10 + 10 + z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + z = 0 + 10
z = 0 + 10

Combine like terms: 0 + 10 = 10
z = 10

Simplifying
z = 10
Solution
z = {0, -10, 10}