z^3+11z^2=0

Solution for z^3+11z^2=0 equation:

Simplifying
z3 + 11z2 = 0

Reorder the terms:
11z2 + z3 = 0

Solving
11z2 + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(11 + 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 '(11 + z)' equal to zero and attempt to solve:

Simplifying
11 + z = 0

Solving
11 + z = 0

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

Add '-11' to each side of the equation.
11 + -11 + z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + z = 0 + -11
z = 0 + -11

Combine like terms: 0 + -11 = -11
z = -11

Simplifying
z = -11
Solution
z = {0, -11}