That this is really, really, really hard.  Way harder than you're thinking.
Sympy can certainly solve them for you, anyway.
Alternatively for polynomial solving, numpy.polynomial.polynomial.polyroots.
And Sympy can do at least differentiation, if Calculus is your cup of tea.  I'm also seeing some support for symbolic integration, and it's probably got a numeric approximator for definite integrals, somewhere, too.
Implementing this yourself will take weeks, and you'll need to read a bunch of academic papers first in all likelihood.  These algorithms are not simple by any stretch of the imagination.

That doesn't matter.  Every equation can be made equal to zero.  if a=b, then a-b=0 for all a and b, whether they be numbers or whatever.  As I read the docs, it's not assuming that the equation is equal to zero, it's setting the equation equal to zero and then solving that.
Edit: yeah, you need to do the transformation yourself.  But even so.

Subtract 22 from both sides?  it's not an actual graphical transformation, just a little algorithm.  Transformation is mathematically the wrong word.  Algebraic manipulation is cumbersome.  Mapping function for equations is completely unhelpful and possibly not even correct vocabulary, but it does at least tickle my internal mathematical correctness conscious.
More generally and more explicitly, assume a and b are functions or terms or numbers or whatever.  Then:

a=b
a-b=b-b
a-b=0

And the last equation still has solutions the same as the first one because all we did is basic algebra.
So, in words, take the right side, subtract it from the left side, and set the resulting thing to 0.
The techniques for actually solving algebraic equations requires a lot of math and theory that you don't have.  I don't have it, either.  For the stuff where it's actually worth using a computer program, you also often end up in the realm of numeric approximation.  For example, Numpy.  We can't actually solve really high degree polynomials with an algorithm, but we can keep approximating the zeros to a really, really precise degree and use them to keep making the polynomial smaller.  When you get to calculus, the published algorithm (not the code, just the description of how to do it) is something or other hundred pages.  Without explanation.  The truth is that if you find using Sympy complex, just imagine rewriting it from scratch, because that's what you're saying you want to do.
Giving you a complete program is not trivial because someone needs to figure out how to parse the input.  I think Sympy also has something for this, but I'm going to leave that as an exercise to the reader.  If nothing else, you can still do it in the Python REPL.  For examples, read the linked page of the Sympy docs, as they show you exactly how.  This is way easier than you are making it.
Edit: I like it when people tell me about my most common, consistent  and obvious spelling mistakes.  I did this one for years too.  Equation is with a t, not an s.  For the record, that's not my worst: my personal worst is ought versus aught, because both are actually words and not flagged by spell check, but aught (with an a) is old English.  And one day I'll stop having to look up which is which.
edit 2: And for those wondering why I care and how I ever found out, I'm on Espeak and Espeak says it really, really wrong with an s.  Really.