Hi, please help!

question is

Find all points on the curve x^2y^2+xy=2 where the slope of the tangent is –1.

d/dx (2x²y) + (2xy²) dy/dx + (y) + (x) dy/dx = 0

Why is " y + x (dy/dx) = 0 " , shouldn't it be " x + y (dy/dx) = 0 " Kindly explain.

dy/dx (2xy² + x) = -2x² y-y

dy/dx = -2x² y-y / 2xy² + x

does it then = x - y / y + x

and does that mean it = -1 because of " = x - y / y + x "

Many thanks for you help if your can explain this!