When we are converting from polar to rectangular form often times in the problems while we are simplifying we divide r from all sides; however, my question is, like how we can't divide x in equations because we might lose a solution, can the same thing happen if r is equal to zero in one case?
An example would be going from $(x^2+y^2)^2-8(x^2-y^2)=0$ to the polar form. While doing this we can divide $r^2$ from both sides to simplify it.