4a^4-16b^4=0

Solution for 4a^4-16b^4=0 equation:

Simplifying
4a4 + -16b4 = 0

Solving
4a4 + -16b4 = 0

Solving for variable 'a'.

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

Add '16b4' to each side of the equation.
4a4 + -16b4 + 16b4 = 0 + 16b4

Combine like terms: -16b4 + 16b4 = 0
4a4 + 0 = 0 + 16b4
4a4 = 0 + 16b4
Remove the zero:
4a4 = 16b4

Divide each side by '4'.
a4 = 4b4

Simplifying
a4 = 4b4

Combine like terms: 4b4 + -4b4 = 0
a4 + -4b4 = 0

Factor a difference between two squares.
(a2 + 2b2)(a2 + -2b2) = 0

Subproblem 1
Set the factor '(a2 + 2b2)' equal to zero and attempt to solve:

Simplifying
a2 + 2b2 = 0

Solving
a2 + 2b2 = 0

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

Add '-2b2' to each side of the equation.
a2 + 2b2 + -2b2 = 0 + -2b2

Combine like terms: 2b2 + -2b2 = 0
a2 + 0 = 0 + -2b2
a2 = 0 + -2b2
Remove the zero:
a2 = -2b2

Simplifying
a2 = -2b2

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 '(a2 + -2b2)' equal to zero and attempt to solve:

Simplifying
a2 + -2b2 = 0

Solving
a2 + -2b2 = 0

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

Add '2b2' to each side of the equation.
a2 + -2b2 + 2b2 = 0 + 2b2

Combine like terms: -2b2 + 2b2 = 0
a2 + 0 = 0 + 2b2
a2 = 0 + 2b2
Remove the zero:
a2 = 2b2

Simplifying
a2 = 2b2

Take the square root of each side:
a = {-1.414213562b, 1.414213562b}
Solution
a = {-1.414213562b, 1.414213562b}