z^3X-6z^2=

Solution for z^3X-6z^2= equation:

Simplifying
z3X + -6z2 = 0

Reorder the terms:
-6z2 + z3X = 0

Solving
-6z2 + z3X = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(-6 + zX) = 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 '(-6 + zX)' equal to zero and attempt to solve:

Simplifying
-6 + zX = 0

Solving
-6 + zX = 0

Move all terms containing z to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + zX = 0 + 6

Combine like terms: -6 + 6 = 0
0 + zX = 0 + 6
zX = 0 + 6

Combine like terms: 0 + 6 = 6
zX = 6

Divide each side by 'X'.
z = 6X-1

Simplifying
z = 6X-1
Solution
z = {0, 6X-1}