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

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

Simplifying
(2r4 + 5r2) + -1(3r4 + -4r2) = 0

Reorder the terms:
(5r2 + 2r4) + -1(3r4 + -4r2) = 0

Remove parenthesis around (5r2 + 2r4)
5r2 + 2r4 + -1(3r4 + -4r2) = 0

Reorder the terms:
5r2 + 2r4 + -1(-4r2 + 3r4) = 0
5r2 + 2r4 + (-4r2 * -1 + 3r4 * -1) = 0
5r2 + 2r4 + (4r2 + -3r4) = 0

Reorder the terms:
5r2 + 4r2 + 2r4 + -3r4 = 0

Combine like terms: 5r2 + 4r2 = 9r2
9r2 + 2r4 + -3r4 = 0

Combine like terms: 2r4 + -3r4 = -1r4
9r2 + -1r4 = 0

Solving
9r2 + -1r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(9 + -1r2) = 0

Factor a difference between two squares.
r2((3 + r)(3 + -1r)) = 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 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 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 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

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

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0, -3, 3}