Question: problem with solving linear eqs

hello
I am doing something about curve fitting. I have got a polynome, I want to have it differentiate on the coefficients A,B,C,D,E,F, then all of these results will be set to zero. so I get 6 eqs,I want to use this 6 eqs to solve the coefficients A to F.  x0,y0,z0 is the coordinate for certain dot. I write the orders as follows:
eq :=(A*x0^2+B*y0^2+C*x0*y0+D*x0+E*y0+F-z0)^2;
S:=map2(diff,eq,[A,B,C,D,E,F]);
solve(S,{A,B,C,D,E,F});
but I got the answer
{A = A, B = B, C = C, D = D, E = E, F = -A*x0^2-B*y0^2-C*x0*y0-D*x0-E*y0+z0}
the answer above may probably the solution of eq; so, how should I handle this problem?
Any help will be appreciated @.@

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