What method can solve the following equation: $6xy -y +x = 16$

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What method can solve the following equation?

$$\forall \, y, x \, \in \mathbb{Z}$$ $$6xy -y +x = 16$$

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Hint: $$6xy-y+x=16$$ $$6\cdot6xy-6y+6x=6\cdot16$$ $$6\cdot6xy-6y+6x-1=6\cdot16-1$$ $$6y(6x-1)+(6x-1)=6\cdot16-1$$ $$(6x-1)(6y+1)=6\cdot16-1$$ $$(6x-1)(6y+1)=95$$