Consider f(x,y) = 2x^2y+xy+2/3(y^3)

Calculated partial derivates fx=4xy+u , fy=2(x^2)+x+2(y^2)

fxx=4y , fxy=4x+1 , fyx=4x+1 , fyy =4y

used partial df/dx =0 = 4xy+y solve y(4x+1)=0 => y=0 x=-1/4

how do I solve partial df/dy= 0 = 2(x^2)+x+2(y^2).

The answer for all stationary points is

(0,0) saddle point; (-1/2, 0 ) saddle point , ( -1/4, 1/4) local min. : (-1/4, -1/4) local min.

Stuck any advice?????