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

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

Simplifying
z3 + -2z2 + 4z = 0

Reorder the terms:
4z + -2z2 + z3 = 0

Solving
4z + -2z2 + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + -2z + z2) = 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 + -2z + z2)' equal to zero and attempt to solve:

Simplifying
4 + -2z + z2 = 0

Solving
4 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + -2z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2z + z2 = 0 + -4
-2z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2z + z2 = -4

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = -4 + 1

Reorder the terms:
1 + -2z + z2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + -2z + z2 = -3

Factor a perfect square on the left side:
(z + -1)(z + -1) = -3

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}