3z^3-6z^2+9z=0

Solution for 3z^3-6z^2+9z=0 equation:

Simplifying
3z3 + -6z2 + 9z = 0

Reorder the terms:
9z + -6z2 + 3z3 = 0

Solving
9z + -6z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(3 + -2z + z2) = 0

Ignore the factor 3.
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 '(3 + -2z + z2)' equal to zero and attempt to solve:

Simplifying
3 + -2z + z2 = 0

Solving
3 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + -2z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z + z2 = 0 + -3
-2z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2z + z2 = -3

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 = -3 + 1

Reorder the terms:
1 + -2z + z2 = -3 + 1

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

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

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}