4a^4b^3-a^2b=0

Solution for 4a^4b^3-a^2b=0 equation:

Simplifying
4a4b3 + -1a2b = 0

Reorder the terms:
-1a2b + 4a4b3 = 0

Solving
-1a2b + 4a4b3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2b'.
a2b(-1 + 4a2b2) = 0

Factor a difference between two squares.
a2b((1 + 2ab)(-1 + 2ab)) = 0

Subproblem 1
Set the factor 'a2b' equal to zero and attempt to solve:

Simplifying
a2b = 0

Solving
a2b = 0

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

Simplifying
a2b = 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 '(1 + 2ab)' equal to zero and attempt to solve:

Simplifying
1 + 2ab = 0

Solving
1 + 2ab = 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 + 2ab = 0 + -1

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

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

Divide each side by '2b'.
a = -0.5b-1

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

Simplifying
-1 + 2ab = 0

Solving
-1 + 2ab = 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 + 2ab = 0 + 1

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

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

Divide each side by '2b'.
a = 0.5b-1

Simplifying
a = 0.5b-1
Solution
a = {-0.5b-1, 0.5b-1}