a^2b=-ab^2

Solution for a^2b=-ab^2 equation:

Simplifying
a2b = -1ab2

Solving
a2b = -1ab2

Solving for variable 'a'.

Reorder the terms:
ab2 + a2b = -1ab2 + ab2

Combine like terms: -1ab2 + ab2 = 0
ab2 + a2b = 0

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(b + 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
Solution
a = {-1b}