Converting polar equations to cartesian

Question

Convert the equation $r\sin(\theta)=-6\sin(2\theta)$ to cartesian coordinates.

I get that $y=r\sin\theta$ so $y=-6\sin(2\theta)$. From there I don't know where to go, so can someone please explain to me how this is converted to $(x+6)^2+y^2=6^2$?

Answer 1

\begin{equation} r\sin(\theta) = -12\sin(\theta)\cos(\theta)\\ r = -12 \cos(\theta)\\ r^2 = -12x\\ x^2 + 12x + y^2 = 0\\ (x+6)^2 - 6^2 + y^2 = 0 \end{equation}