0=-z^3(9-z)+4z(2+3z)

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Solution for 0=-z^3(9-z)+4z(2+3z) equation: 


Simplifying
0 = -1z3(9 + -1z) + 4z(2 + 3z)
0 = (9 * -1z3 + -1z * -1z3) + 4z(2 + 3z)
0 = (-9z3 + 1z4) + 4z(2 + 3z)
0 = -9z3 + 1z4 + (2 * 4z + 3z * 4z)
0 = -9z3 + 1z4 + (8z + 12z2)

Reorder the terms:
0 = 8z + 12z2 + -9z3 + 1z4

Solving
0 = 8z + 12z2 + -9z3 + 1z4

Solving for variable 'z'.
Remove the zero:
-8z + -12z2 + 9z3 + -1z4 = 8z + 12z2 + -9z3 + 1z4 + -8z + -12z2 + 9z3 + -1z4

Reorder the terms:
-8z + -12z2 + 9z3 + -1z4 = 8z + -8z + 12z2 + -12z2 + -9z3 + 9z3 + 1z4 + -1z4

Combine like terms: 8z + -8z = 0
-8z + -12z2 + 9z3 + -1z4 = 0 + 12z2 + -12z2 + -9z3 + 9z3 + 1z4 + -1z4
-8z + -12z2 + 9z3 + -1z4 = 12z2 + -12z2 + -9z3 + 9z3 + 1z4 + -1z4

Combine like terms: 12z2 + -12z2 = 0
-8z + -12z2 + 9z3 + -1z4 = 0 + -9z3 + 9z3 + 1z4 + -1z4
-8z + -12z2 + 9z3 + -1z4 = -9z3 + 9z3 + 1z4 + -1z4

Combine like terms: -9z3 + 9z3 = 0
-8z + -12z2 + 9z3 + -1z4 = 0 + 1z4 + -1z4
-8z + -12z2 + 9z3 + -1z4 = 1z4 + -1z4

Combine like terms: 1z4 + -1z4 = 0
-8z + -12z2 + 9z3 + -1z4 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-8 + -12z + 9z2 + -1z3) = 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 '(-8 + -12z + 9z2 + -1z3)' equal to zero and attempt to solve:

Simplifying
-8 + -12z + 9z2 + -1z3 = 0

Solving
-8 + -12z + 9z2 + -1z3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}

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