Z^3=Z^2+30Z

Solution for Z^3=Z^2+30Z equation:

Simplifying
Z3 = Z2 + 30Z

Reorder the terms:
Z3 = 30Z + Z2

Solving
Z3 = 30Z + Z2

Solving for variable 'Z'.

Reorder the terms:
-30Z + -1Z2 + Z3 = 30Z + Z2 + -30Z + -1Z2

Reorder the terms:
-30Z + -1Z2 + Z3 = 30Z + -30Z + Z2 + -1Z2

Combine like terms: 30Z + -30Z = 0
-30Z + -1Z2 + Z3 = 0 + Z2 + -1Z2
-30Z + -1Z2 + Z3 = Z2 + -1Z2

Combine like terms: Z2 + -1Z2 = 0
-30Z + -1Z2 + Z3 = 0

Factor out the Greatest Common Factor (GCF), 'Z'.
Z(-30 + -1Z + Z2) = 0

Factor a trinomial.
Z((-5 + -1Z)(6 + -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 '(-5 + -1Z)' equal to zero and attempt to solve:

Simplifying
-5 + -1Z = 0

Solving
-5 + -1Z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1Z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1Z = 0 + 5
-1Z = 0 + 5

Combine like terms: 0 + 5 = 5
-1Z = 5

Divide each side by '-1'.
Z = -5

Simplifying
Z = -5
Subproblem 3
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
Solution
Z = {0, -5, 6}