225+516r^2-21r^4=0

Solution for 225+516r^2-21r^4=0 equation:

Simplifying
225 + 516r2 + -21r4 = 0

Solving
225 + 516r2 + -21r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(75 + 172r2 + -7r4) = 0

Factor a trinomial.
3((25 + -1r2)(3 + 7r2)) = 0

Factor a difference between two squares.
3(((5 + r)(5 + -1r))(3 + 7r2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 7r2)' equal to zero and attempt to solve:

Simplifying
3 + 7r2 = 0

Solving
3 + 7r2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7r2 = 0 + -3
7r2 = 0 + -3

Combine like terms: 0 + -3 = -3
7r2 = -3

Divide each side by '7'.
r2 = -0.4285714286

Simplifying
r2 = -0.4285714286

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

Simplifying
5 + r = 0

Solving
5 + r = 0

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

Add '-5' to each side of the equation.
5 + -5 + r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Subproblem 3
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-5, 5}