kill(all)$

fpprintprec:3$

van=facebook.com/
LearningCalculus$

f(x,y,z):=x^2-2*y*z-z-x$
g(x,y,z):=y^2-2*z*x-x-y$
h(x,y,z):=z^2-2*x*z-y-z$

F(x,y,z):=
[f(x,y,z),
 g(x,y,z),
 h(x,y,z)]$

s:solve
([f(x,y,z),
  g(x,y,z),
  h(x,y,z)],[x,y,z])$

s[1];
s[2];
s[7];
s[8];

F(0,0,0);
F(-2,-2,-2);