x=rcos(θ)
y=rsin(θ)
r2=x2+y2
Make the necessary substitutions
3rsin(θ)=2(rcos(θ))2−2rcos(θ)rsin(θ)−rcos(θ)
Simplify
3rsin(θ)=2r2cos2(θ)−2r2cos(θ)sin(θ)−rcos(θ)
Add rcos(θ) to both sides
3rsin(θ)+rcos(θ)=2r2cos2(θ)−2r2cos(θ)sin(θ)
Factor out r and r2
r(3sin(θ)+cos(θ))=r2(2cos2(θ)−2cos(θ)sin(θ))
Isolated r2
r(3sin(θ)+cos(θ))2cos2(θ)−2cos(θ)sin(θ)=r22cos2(θ)−2cos(θ)sin(θ)2cos2(θ)−2cos(θ)sin(θ)
r(3sin(θ)+cos(θ))2cos2(θ)−2cos(θ)sin(θ)=r2
Gather r to the right hand side
r(3sin(θ)+cos(θ))2cos2(θ)−2cos(θ)sin(θ)r=r2r
Simplify
3sin(θ)+cos(θ)2cos2(θ)−2cos(θ)sin(θ)=r
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