a^2(3a-1)=0

Solution for a^2(3a-1)=0 equation:

Simplifying
a2(3a + -1) = 0

Reorder the terms:
a2(-1 + 3a) = 0
(-1 * a2 + 3a * a2) = 0
(-1a2 + 3a3) = 0

Solving
-1a2 + 3a3 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-1 + 3a)' equal to zero and attempt to solve:

Simplifying
-1 + 3a = 0

Solving
-1 + 3a = 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 + 3a = 0 + 1

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

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

Divide each side by '3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {0, 0.3333333333}