First off, you should never use Out[] except when working interactively. The numbers in the brackets change. Once you have fixed this, the rest might make more sense.

Also, while it is neat to use greek letters, for plain code, they make the code less clear -- never a good thing. If you want alpha to show up in the UI, then there is an option in manipulate to display the greek letter while the code uses an ascii letter.

Finally, you really should not start your variable names with a capital letter. Wolfram Language uses a surprising number of them both internally and externally.

Here are some improvement suggestions: 1) you should use Definition if it is really a definition to be evaluated later on. f[Z_] is not proper in your code and you should write it as f[Z] instead because you use simple assignment rule. 2) do not use single Capital letters for variable names as they may interfere with Mathematica global variables 3) use single Simplify command to reduce the number of equations in one simple equations={eq1, eq2, ...eq13}//Simplify 4) Manipulate[ FindRoot[equations, ...], followed by parameter sliders

Hope this helps

Jones

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

thank you very much, the last thing I would like to know is if I can somehow make it show me the values of Manipulate [] as tables.

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