z^3+100z-z^2-100z=0

Solution for z^3+100z-z^2-100z=0 equation:

Simplifying
z3 + 100z + -1z2 + -100z = 0

Reorder the terms:
100z + -100z + -1z2 + z3 = 0

Combine like terms: 100z + -100z = 0
0 + -1z2 + z3 = 0
-1z2 + z3 = 0

Solving
-1z2 + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(-1 + z) = 0

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 '(-1 + z)' equal to zero and attempt to solve:

Simplifying
-1 + z = 0

Solving
-1 + z = 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 + z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + z = 0 + 1
z = 0 + 1

Combine like terms: 0 + 1 = 1
z = 1

Simplifying
z = 1
Solution
z = {0, 1}