4a^3-a=0

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

Simplifying
4a3 + -1a = 0

Reorder the terms:
-1a + 4a3 = 0

Solving
-1a + 4a3 = 0

Solving for variable 'a'.

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

Factor a difference between two squares.
a((1 + 2a)(-1 + 2a)) = 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 '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

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

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

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

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

Simplifying
-1 + 2a = 0

Solving
-1 + 2a = 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 + 2a = 0 + 1

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

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

Divide each side by '2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {0, -0.5, 0.5}