a^3b-9a^2b^2+20ab^3=0

Solution for a^3b-9a^2b^2+20ab^3=0 equation:

Simplifying
a3b + -9a2b2 + 20ab3 = 0

Reorder the terms:
20ab3 + -9a2b2 + a3b = 0

Solving
20ab3 + -9a2b2 + a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(20b2 + -9ab + a2) = 0

Factor a trinomial.
ab((4b + -1a)(5b + -1a)) = 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 '(4b + -1a)' equal to zero and attempt to solve:

Simplifying
4b + -1a = 0

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

Solving
-1a + 4b = 0

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

Add '-4b' to each side of the equation.
-1a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
-1a + 0 = 0 + -4b
-1a = 0 + -4b
Remove the zero:
-1a = -4b

Divide each side by '-1'.
a = 4b

Simplifying
a = 4b
Subproblem 3
Set the factor '(5b + -1a)' equal to zero and attempt to solve:

Simplifying
5b + -1a = 0

Reorder the terms:
-1a + 5b = 0

Solving
-1a + 5b = 0

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

Add '-5b' to each side of the equation.
-1a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
-1a + 0 = 0 + -5b
-1a = 0 + -5b
Remove the zero:
-1a = -5b

Divide each side by '-1'.
a = 5b

Simplifying
a = 5b
Solution
a = {4b, 5b}