-32z^5+32z^4+10z^3=

Solution for -32z^5+32z^4+10z^3= equation:

Simplifying
-32z5 + 32z4 + 10z3 = 0

Reorder the terms:
10z3 + 32z4 + -32z5 = 0

Solving
10z3 + 32z4 + -32z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z3'.
2z3(5 + 16z + -16z2) = 0

Factor a trinomial.
2z3((5 + -4z)(1 + 4z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve:

Simplifying
z3 = 0

Solving
z3 = 0

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

Simplifying
z3 = 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 '(5 + -4z)' equal to zero and attempt to solve:

Simplifying
5 + -4z = 0

Solving
5 + -4z = 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 + -4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z = 0 + -5
-4z = 0 + -5

Combine like terms: 0 + -5 = -5
-4z = -5

Divide each side by '-4'.
z = 1.25

Simplifying
z = 1.25
Subproblem 3
Set the factor '(1 + 4z)' equal to zero and attempt to solve:

Simplifying
1 + 4z = 0

Solving
1 + 4z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z = 0 + -1
4z = 0 + -1

Combine like terms: 0 + -1 = -1
4z = -1

Divide each side by '4'.
z = -0.25

Simplifying
z = -0.25
Solution
z = {1.25, -0.25}