I think I posted this before, but just in case this thread comes up in a search this is how I install my hp printer:
Dependencies are HPLIP-DRIVERS and Python-distro. The Solus 4.3 and 4.4 ISO installs them, but check anyway.
Install HPLIP from the software center.
Type hp-setup in the terminal.
I've never had it automatically detect my networked printer, so I go into advanced and enter the network address and it goes from there.
I've had no luck with the tarball or whatever from HP on any distro. Last time I tried I think there was some sudo issue.