(3r^4+3r^2)-(5r^6+6r^2)=

Solution for (3r^4+3r^2)-(5r^6+6r^2)= equation:

Simplifying
(3r4 + 3r2) + -1(5r6 + 6r2) = 0

Reorder the terms:
(3r2 + 3r4) + -1(5r6 + 6r2) = 0

Remove parenthesis around (3r2 + 3r4)
3r2 + 3r4 + -1(5r6 + 6r2) = 0

Reorder the terms:
3r2 + 3r4 + -1(6r2 + 5r6) = 0
3r2 + 3r4 + (6r2 * -1 + 5r6 * -1) = 0
3r2 + 3r4 + (-6r2 + -5r6) = 0

Reorder the terms:
3r2 + -6r2 + 3r4 + -5r6 = 0

Combine like terms: 3r2 + -6r2 = -3r2
-3r2 + 3r4 + -5r6 = 0

Solving
-3r2 + 3r4 + -5r6 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-3 + 3r2 + -5r4) = 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 '(-3 + 3r2 + -5r4)' equal to zero and attempt to solve:

Simplifying
-3 + 3r2 + -5r4 = 0

Solving
-3 + 3r2 + -5r4 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.6 + -0.6r2 + r4 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.6r2 + -0.6 + r4 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.6r2 + r4 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.6r2 + r4 = 0 + -0.6
-0.6r2 + r4 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.6r2 + r4 = -0.6

The r term is -0.6r2.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6r2 + 0.09 + r4 = -0.6 + 0.09

Reorder the terms:
0.09 + -0.6r2 + r4 = -0.6 + 0.09

Combine like terms: -0.6 + 0.09 = -0.51
0.09 + -0.6r2 + r4 = -0.51

Factor a perfect square on the left side:
(r2 + -0.3)(r2 + -0.3) = -0.51

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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