`x^2 + 2xy + x +1 +3y = 15`
`⇔x^2 + 2xy + x +3y = 14`
`⇔x(x+1)=14-y(2x+3)`
`⇔x^2+x-14=-y(2x+3)`
`⇔`\begin{cases}x^2+x-14 \vdots y\\x^2+x-14 \vdots 2x+3 \end{cases}
`⇔`\begin{cases}x^2+x-14 \vdots y\\4x^2+4x-56 \vdots 2x+3 \end{cases}
`⇔`\begin{cases}x^2+x-14 \vdots y\\(2x+3)(2x-1)-53\vdots 2x+3 \end{cases}
`⇔53\vdots 2x+3`
`⇔2x+3∈Ư(53)`
`⇔2x+3={±1;±53}`
`⇔x={-28;-2;-1;25}`
`+)`với` x=-28`
`⇒y=14`
`+)`với` x=-2`
`⇒y=-12`
`+)`với` x=-1`
`⇒y=14`
`+)`với` x=25`
`⇒y=-12`
