z^3-6z^2=72z

Solution for z^3-6z^2=72z equation:

Simplifying
z3 + -6z2 = 72z

Reorder the terms:
-6z2 + z3 = 72z

Solving
-6z2 + z3 = 72z

Solving for variable 'z'.

Reorder the terms:
-72z + -6z2 + z3 = 72z + -72z

Combine like terms: 72z + -72z = 0
-72z + -6z2 + z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-72 + -6z + z2) = 0

Factor a trinomial.
z((-6 + -1z)(12 + -1z)) = 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 '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 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 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

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

Simplifying
z = -6
Subproblem 3
Set the factor '(12 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

Simplifying
z = 12
Solution
z = {0, -6, 12}