What's The Best Way To Factor This?

\[\large 3x + 2y = xy \]

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

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