3a^3-4a=0

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

Simplifying
3a3 + -4a = 0

Reorder the terms:
-4a + 3a3 = 0

Solving
-4a + 3a3 = 0

Solving for variable 'a'.

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

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 '(-4 + 3a2)' equal to zero and attempt to solve:

Simplifying
-4 + 3a2 = 0

Solving
-4 + 3a2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3a2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3a2 = 0 + 4
3a2 = 0 + 4

Combine like terms: 0 + 4 = 4
3a2 = 4

Divide each side by '3'.
a2 = 1.333333333

Simplifying
a2 = 1.333333333

Take the square root of each side:
a = {-1.154700538, 1.154700538}
Solution
a = {0, -1.154700538, 1.154700538}