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

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

Simplifying
-3z(4z2 + -4) = 0

Reorder the terms:
-3z(-4 + 4z2) = 0
(-4 * -3z + 4z2 * -3z) = 0
(12z + -12z3) = 0

Solving
12z + -12z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '12z'.
12z(1 + -1z2) = 0

Factor a difference between two squares.
12z((1 + z)(1 + -1z)) = 0

Ignore the factor 12.
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 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

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

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

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

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

Simplifying
1 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {0, -1, 1}