Implicit Equations

I'm semi-new to text-based coding and i have no experience with using implicit equations in any for of coding. really want to make a calculator to simplify a given implicit equation, but i don't know how to use implicit equations. I'm also not looking to graph them (like an implicit equation of x and y), im just looking to simplify them instead.

Thank you in advance! ⚞(^•ᆺ•^)⚟