What's The Best Way To Factor This?

Number Theory Level 4

$\large 3x + 2y = xy$

Let $(x_1,y_1), (x_2,y_2), \ldots, (x_n,y_n)$ be all the pairs of positive integer roots $(x,y)$ that satisfy the equation above.

Find $(x_1 + x_2 + \cdots +x_n) + (y_1 + y_2 + \cdots + y_n)$ .