-z^3+4z^2-5z=0

Solution for -z^3+4z^2-5z=0 equation:

Simplifying
-1z3 + 4z2 + -5z = 0

Reorder the terms:
-5z + 4z2 + -1z3 = 0

Solving
-5z + 4z2 + -1z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-5 + 4z + -1z2) = 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 '(-5 + 4z + -1z2)' equal to zero and attempt to solve:

Simplifying
-5 + 4z + -1z2 = 0

Solving
-5 + 4z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -4z + z2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -4z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + -4z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z + z2 = 0 + -5
-4z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4z + z2 = -5

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = -5 + 4

Reorder the terms:
4 + -4z + z2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + -4z + z2 = -1

Factor a perfect square on the left side:
(z + -2)(z + -2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}