z^3+6z^2=0

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

Simplifying
z3 + 6z2 = 0

Reorder the terms:
6z2 + z3 = 0

Solving
6z2 + z3 = 0

Solving for variable 'z'.

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

Simplifying
6 + z = 0

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

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

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

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