a^3b-ab^3=0

Solution for a^3b-ab^3=0 equation:

Simplifying
a3b + -1ab3 = 0

Reorder the terms:
-1ab3 + a3b = 0

Solving
-1ab3 + a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(-1b2 + a2) = 0

Factor a difference between two squares.
ab((b + a)(-1b + a)) = 0

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

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(b + a)' equal to zero and attempt to solve:

Simplifying
b + a = 0

Reorder the terms:
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

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

Simplifying
-1b + a = 0

Reorder the terms:
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Solution
a = {-1b, b}