z^3=16z

Solution for z^3=16z equation:

Simplifying
z3 = 16z

Solving
z3 = 16z

Solving for variable 'z'.

Reorder the terms:
-16z + z3 = 16z + -16z

Combine like terms: 16z + -16z = 0
-16z + z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-16 + z2) = 0

Factor a difference between two squares.
z((4 + z)(-4 + z)) = 0

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 '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 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 + z = 0 + -4

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

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

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

Simplifying
-4 + z = 0

Solving
-4 + z = 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 + z = 0 + 4

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

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

Simplifying
z = 4
Solution
z = {0, -4, 4}