(4r^3+4r)-(3r^3-2r)=0

Solution for (4r^3+4r)-(3r^3-2r)=0 equation:

Simplifying
(4r3 + 4r) + -1(3r3 + -2r) = 0

Reorder the terms:
(4r + 4r3) + -1(3r3 + -2r) = 0

Remove parenthesis around (4r + 4r3)
4r + 4r3 + -1(3r3 + -2r) = 0

Reorder the terms:
4r + 4r3 + -1(-2r + 3r3) = 0
4r + 4r3 + (-2r * -1 + 3r3 * -1) = 0
4r + 4r3 + (2r + -3r3) = 0

Reorder the terms:
4r + 2r + 4r3 + -3r3 = 0

Combine like terms: 4r + 2r = 6r
6r + 4r3 + -3r3 = 0

Combine like terms: 4r3 + -3r3 = 1r3
6r + 1r3 = 0

Solving
6r + 1r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(6 + r2) = 0

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(6 + r2)' equal to zero and attempt to solve:

Simplifying
6 + r2 = 0

Solving
6 + r2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r2 = 0 + -6
r2 = 0 + -6

Combine like terms: 0 + -6 = -6
r2 = -6

Simplifying
r2 = -6

The solution to this equation could not be determined.

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