<s>[INST] $y^2+5xy+6x^2-9x-4y=0$ where $x$ and $y$ are integers Need some help solving this for integers $x$ and $y$:
$$
y^2+5xy+6x^2-9x-4y=0
$$
I managed to make something like this:
$$
(y+3x-4)(y+2x)=x\\
(y+3x)(y+2x-3)=y
$$
Find integers for $x$ and $y$ that satisfy the equations above.
But, what do I do next, or is this a bad approach?
 [/INST] $$  (y+3x -3)(y+2x - 1)= y^2 + 5 yx + 6 x^2 -9x-4y +3  $$
$$  (y+3x -3)(y+2x - 1)= 3  $$
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