r^4+16r^2=0

Solution for r^4+16r^2=0 equation:

Simplifying
r4 + 16r2 = 0

Reorder the terms:
16r2 + r4 = 0

Solving
16r2 + r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(16 + r2) = 0

Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}
Subproblem 2
Set the factor '(16 + r2)' equal to zero and attempt to solve:

Simplifying
16 + r2 = 0

Solving
16 + r2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + r2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + r2 = 0 + -16
r2 = 0 + -16

Combine like terms: 0 + -16 = -16
r2 = -16

Simplifying
r2 = -16

The solution to this equation could not be determined.

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