8r^4-r^2=

Solution for 8r^4-r^2= equation:

Simplifying
8r4 + -1r2 = 0

Reorder the terms:
-1r2 + 8r4 = 0

Solving
-1r2 + 8r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-1 + 8r2) = 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 '(-1 + 8r2)' equal to zero and attempt to solve:

Simplifying
-1 + 8r2 = 0

Solving
-1 + 8r2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 8r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8r2 = 0 + 1
8r2 = 0 + 1

Combine like terms: 0 + 1 = 1
8r2 = 1

Divide each side by '8'.
r2 = 0.125

Simplifying
r2 = 0.125

Take the square root of each side:
r = {-0.353553391, 0.353553391}
Solution
r = {0, -0.353553391, 0.353553391}