“Algebra” by itself is meaninglessly broad. You could certainly teach “solve [some simple kinds of] equations for an unknown” in a few months; you could also have a whole mathematical career as an algebraist.
The term is not meaninglessly broad here in the US. We use the term "abstract algebra" to describe the more general subject, usually taught in college-level courses in groups, fields, and so on. Mere 'algebra' does indeed mostly mean "solving for an unknown", although I'd argue there's an important, more general concept of 'equation' introduced. From what I've read the concept of 'variable' is tricky for a lot of kids.
Here's the HS math sequence options from my local school district in VA. Can't speak to many other places but this is what my above comment is based on.
Only one of those options will even leave you remotely prepared for college level mathematics. The fact it stops at Algebra 2 or Part 2 for most of those options is criminal.
