i\'m stuck at this very basic form, that i could not accomplish, which i want to build a search form with an text input, and two select controls, with a route that accept 3
So you're trying to get the search term and category into the URL?
I would advise against this as you'll have to deal with multi-word search terms etc, and could end up with all manner of unpleasantness with disallowed characters.
I would suggest POSTing the data, sanitising it and then returning a results page.
Laravel routing is not designed to accept GET requests from forms, it is designed to use URL segments as get parameters, and built around that idea.