-12z^3+12z^2-3z=0

Solution for -12z^3+12z^2-3z=0 equation:

Simplifying
-12z3 + 12z2 + -3z = 0

Reorder the terms:
-3z + 12z2 + -12z3 = 0

Solving
-3z + 12z2 + -12z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-1 + 4z + -4z2) = 0

Factor a trinomial.
3z((-1 + 2z)(1 + -2z)) = 0

Ignore the factor 3.
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 + 2z)' equal to zero and attempt to solve:

Simplifying
-1 + 2z = 0

Solving
-1 + 2z = 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 + 2z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2z = 0 + 1
2z = 0 + 1

Combine like terms: 0 + 1 = 1
2z = 1

Divide each side by '2'.
z = 0.5

Simplifying
z = 0.5
Subproblem 3
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {0, 0.5, 0.5}