You have defined x to be a function of Pn only, but in fact, it is dependent on several other parameters and you are not passing those values into the function. So, they are global. But inside Manipulate, they are local control variables. One way to address this is to make sure all of your functions pass in all of the parameter values:

x[Pn_, h_, d_] := (h (d/Pn)^d)^(1/(1 - d));

nx[Pn_, h_, d_] := d/Pn x[Pn, h, d];

Bx[Pn_, h_, d_] := (1 - d)*x[Pn, h, d];

f[z_] := -0.0003*z^3 + 0.006*z^2 - 0.1*z + 1;

n[Pn_, k_, h_, d_] := k f[x[Pn, h, d]];

Bn[Pn_, k_, h_, d_] := Pn n[Pn, k, h, d];

r[Pn_, k_, h_, d_] := Bx[Pn, h, d] + Bn[Pn, k, h, d];

xc[Pn_, a_, k_, h_, d_] := a r[Pn, k, h, d];

nc[Pn_, a_, k_, h_, d_] := (1 - a)/Pn r[Pn, k, h, d];

eq[Pn_, k_, a_, h_, d_] := 
  n[Pn, k, h, d] - nc[Pn, a, k, h, d] - nx[Pn, h, d];

Manipulate[
 FindRoot[eq[Pn, k, a, h, d] == 0, {Pn, 0.5966337871664869`}], {h, 4, 
  5}, {d, 0.3, 2}, {a, 0.5, 1}, {k, 20, 100}]

the problem is that I have not managed to run me otherwise, everything works perfectly but fails to work me without using the OUT [%] also would eliminate all that and the program work without placing me Simplify[]

Thx