Turning points of y^3+3xy-x^3=3 (fun differentiation problem! :D)?

Need to differentiate here, find where the gradient equals zero, I'll be very grateful if anyone could explain the later steps, I was a little shaky when it came to setting an equation with x's and y's in equal to zero. You'll see if you do it, hopefully, otherwise i've gone majorly wrong! cheers! :D