4a^3b-40a^2b^2+100ab^3=0

Solution for 4a^3b-40a^2b^2+100ab^3=0 equation:

Simplifying
4a3b + -40a2b2 + 100ab3 = 0

Reorder the terms:
100ab3 + -40a2b2 + 4a3b = 0

Solving
100ab3 + -40a2b2 + 4a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4ab'.
4ab(25b2 + -10ab + a2) = 0

Factor a trinomial.
4ab((5b + -1a)(5b + -1a)) = 0

Ignore the factor 4.
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 '(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
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 = {5b, 5b}