12a^3-4a=0

Solution for 12a^3-4a=0 equation:

Simplifying
12a3 + -4a = 0

Reorder the terms:
-4a + 12a3 = 0

Solving
-4a + 12a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-1 + 3a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-1 + 3a2)' equal to zero and attempt to solve:

Simplifying
-1 + 3a2 = 0

Solving
-1 + 3a2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3a2 = 0 + 1
3a2 = 0 + 1

Combine like terms: 0 + 1 = 1
3a2 = 1

Divide each side by '3'.
a2 = 0.3333333333

Simplifying
a2 = 0.3333333333

Take the square root of each side:
a = {-0.577350269, 0.577350269}
Solution
a = {0, -0.577350269, 0.577350269}