4a^3+16ab^2=0

Solution for 4a^3+16ab^2=0 equation:

Simplifying
4a3 + 16ab2 = 0

Reorder the terms:
16ab2 + 4a3 = 0

Solving
16ab2 + 4a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(4b2 + a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(4b2 + a2)' equal to zero and attempt to solve:

Simplifying
4b2 + a2 = 0

Reorder the terms:
a2 + 4b2 = 0

Solving
a2 + 4b2 = 0

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

Add '-4b2' to each side of the equation.
a2 + 4b2 + -4b2 = 0 + -4b2

Combine like terms: 4b2 + -4b2 = 0
a2 + 0 = 0 + -4b2
a2 = 0 + -4b2
Remove the zero:
a2 = -4b2

Simplifying
a2 = -4b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}