(z^9)+(3z^8)=0

Solution for (z^9)+(3z^8)=0 equation:

Simplifying
(z9) + (3z8) = 0
z9 + (3z8) = 0

Reorder the terms:
(3z8) + z9 = 0

Solving
(3z8) + z9 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z8'.
z8(3 + z) = 0

Subproblem 1
Set the factor 'z8' equal to zero and attempt to solve:

Simplifying
z8 = 0

Solving
z8 = 0

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

Simplifying
z8 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-3}