How many integer solutions does the equation 2xy + 3x + 5y + 7 = 0 have?

Let’s transform the equation:

2xy + 3x + 5y + 7 = 0;
x (2y + 3) = -5y – 7;
x = (-5y – 7) / (2y + 3);
2x = (-10y – 14) / (2y + 3);
2x = (-10y – 15 + 1) / (2y + 3);
2x = (-5 (2y + 3) + 1) / (2y + 3);
2x = -5 + 1 / (2y + 3).
The denominator can be -1 and 1:

1)

{2y + 3 = -1;
{2x = -5 – 1;
{2y = -4;
{2x = -6;
{y = -2;
{x = -3.
2)

{2y + 3 = 1;
{2x = -5 + 1;
{2y = -2;
{2x = -4;
{y = -1;
{x = -2.