What is number of pairs of natural numbers $(x,y)$ which satisfy the equation $2x(xy-2y-3)=(x+y)(3x+y)$?
I factored the equation into a quadratic in $y$ and then use the discriminant(D) condition ($D \geq 0$ and $D$ should be a perfect square) but this is lengthy.
Could someone please suggest a simpler way. Thanks!