r^4-16s^4=0

Solution for r^4-16s^4=0 equation:

Simplifying
r4 + -16s4 = 0

Solving
r4 + -16s4 = 0

Solving for variable 'r'.

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

Add '16s4' to each side of the equation.
r4 + -16s4 + 16s4 = 0 + 16s4

Combine like terms: -16s4 + 16s4 = 0
r4 + 0 = 0 + 16s4
r4 = 0 + 16s4
Remove the zero:
r4 = 16s4

Simplifying
r4 = 16s4

Combine like terms: 16s4 + -16s4 = 0
r4 + -16s4 = 0

Factor a difference between two squares.
(r2 + 4s2)(r2 + -4s2) = 0

Factor a difference between two squares.
(r2 + 4s2)((r + 2s)(r + -2s)) = 0

Subproblem 1
Set the factor '(r2 + 4s2)' equal to zero and attempt to solve:

Simplifying
r2 + 4s2 = 0

Solving
r2 + 4s2 = 0

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

Add '-4s2' to each side of the equation.
r2 + 4s2 + -4s2 = 0 + -4s2

Combine like terms: 4s2 + -4s2 = 0
r2 + 0 = 0 + -4s2
r2 = 0 + -4s2
Remove the zero:
r2 = -4s2

Simplifying
r2 = -4s2

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 '(r + 2s)' equal to zero and attempt to solve:

Simplifying
r + 2s = 0

Solving
r + 2s = 0

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

Add '-2s' to each side of the equation.
r + 2s + -2s = 0 + -2s

Combine like terms: 2s + -2s = 0
r + 0 = 0 + -2s
r = 0 + -2s
Remove the zero:
r = -2s

Simplifying
r = -2s
Subproblem 3
Set the factor '(r + -2s)' equal to zero and attempt to solve:

Simplifying
r + -2s = 0

Solving
r + -2s = 0

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

Add '2s' to each side of the equation.
r + -2s + 2s = 0 + 2s

Combine like terms: -2s + 2s = 0
r + 0 = 0 + 2s
r = 0 + 2s
Remove the zero:
r = 2s

Simplifying
r = 2s
Solution
r = {-2s, 2s}