Question: solve equations

Hi I will appreciate some help

I am trying to find the algebraic solution of the equation and want to express z in terms of c

z1 := 819*z^6+(-396+396*c)*z^4+306*z^3*c+(63*c^2-126*c+63)*z^2+(90*c^2-90*c)*z+6*c^3-9*c^2+18*c-6;

i use solve(z1=0,z) but i got

[z=RootOf(273 _Z^6+(-132+132 c) _Z^4+102 _Z^3 c+(-42 c+21+21 c^2) _Z^2+(-30 c+30 c^2) _Z-2+2 c^3-3 c^2+6 c).

Can anyone help?

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