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Matlab and GNU Octave can do symbolic equation solving:

Matlab is a nice, but expensive commercial product.

GNU Octave is free software (libre and gratis):

Scilab is free, reliable and very similar to Matlab. I believe an arm of the French Government is responsible for it.

I use an old hp48gx calculator which can convert a program into an algebraic expression. The calculator can be downloaded free. Search for emu48

I will definitely look into it!

"symbolic equation solving" was the term that helped me refine my search. Thanks!