Answer
$9x^2+5y^2-36-24y=0$
Work Step by Step
After multiplying with the denominator of the fraction: $r(3-2\sin{\theta})=6\\3r-2r\sin{\theta}=6\\3r=6+2r\sin{\theta}\\9r^2=(6+2r\sin{\theta})^2$.
We know that $r^2=x^2+y^2$ and that $x=r\cos\theta,y=r\sin\theta$.
Hence $9r^2=(6+2r\sin{\theta})^2$ becomes: $9(x^2+y^2)=(6+2y)^2\\9x^2+9y^2=36+24y+4y^2\\9x^2+5y^2-36-24y=0$
