Hey anyone know how I can solve this?

The equation is (x^2)+2x+(y^4)+4y=5

How do I find the coordinates of the two points on the curve where the line tangent to the curve is vertical?

Also, is it possible for this curve to have a horizontal tangent line at the points where it intersects the x-axis? Why or why not?

Any explanations would be great so I could learn how to approach this problem in the future. Thanks!