-96z^3+48z^2-6z=

Solution for -96z^3+48z^2-6z= equation:

Simplifying
-96z3 + 48z2 + -6z = 0

Reorder the terms:
-6z + 48z2 + -96z3 = 0

Solving
-6z + 48z2 + -96z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '6z'.
6z(-1 + 8z + -16z2) = 0

Factor a trinomial.
6z((-1 + 4z)(1 + -4z)) = 0

Ignore the factor 6.
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 '(-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
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 = {0, 0.25, 0.25}