$2xy+x+2y=4$
$⇒2y(x+1)+(x+1)=5$
$⇒(x+1)(2y+1)=5$
TH1: $\left \{ {{x+1=1} \atop {2y+1=5}} \right.$ =>$\left \{ {{x=0} \atop {y=2}} \right.$
TH2: $\left \{ {{x+1=-1} \atop {2y+1=-5}} \right.$ =>$\left \{ {{x=-2} \atop {y=-3}} \right.$
TH3: $\left \{ {{x+1=5} \atop {2y+1=1}} \right.$ =>$\left \{ {{x=4} \atop {y=0}} \right.$
TH4: $\left \{ {{x+1=-5} \atop {2y+1=-1}} \right.$ =>$\left \{ {{x=-6} \atop {y=-1}} \right.$
Vậy (x,y)∈{(0;2);(-2;-3);(4;0);(-6;-1)}
