what values of c is the locus of the function (x^2+x+y+3)y+z(x+y+3)+c a surface?

ok so my f=yx^2+yx+y^2+3y+zx+zy+3z+c..

i know that on a surface df cant equal zero..

my df=(2xy+y+z)dx+(x^2+x+2y+3)dy+(x+y+3)dz...

so how do i find c, if df cant equal zero?

but if x=y=z=0 df is 0, and it not 0 if c equals all reals except 0?