\(x+2xy+3y=6\)
\(4xy+2x+6y=12\)
\(2x\left(2y+1\right)+3\left(2y+1\right)=12+3\)
\(\left(2x+3\right)\left(2y+1\right)=15\)
\(2x+3\inƯ\left(15\right)=\left\{1;3;5;15\right\}\)
Mà 2x + 3 > 1
Từ đó tìm được \(\left(x;y\right)\in\left\{\left(0;2\right),\left(1;1\right),\left(6;0\right)\right\}\)