II've googled and it seems this package - hplip-3.16.7.run - could help me, but during the installation it asks to choose from a list of distros. I tried to install under Debian and Ubuntu and in both situations the installation stops when a error message appears: "no gcc". Please, can anybody help?

have you tried sudo apt install gcc

Hey try this! I was able to install my HP Inktank 415.

What I did was:
- Downloaded the HPLIP and extracted
- manually added a printer through the Deepin Printer Settings by clicking "+ Add"
- then selected my printer from the network printer (the one with the IP Address and selected "AppSocket/HP JetDirect"
- Clicked "Forward" then on the next window selected Provide PPD Fileand browsed on the HPLIP extracted folder under PPD/HPCups and selected the file named after my printer model with "PD" file extension

I've tried!
carlos@carlos-PC:~$ sudo apt install gcc
Reading package lists... Done
Building dependency tree      
Reading state information... Done
gcc is already the newest version (4:7.3.0-3).
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

But when I run the program it does not find the installed version!

I've tried!
carlos@carlos-PC:~$ sudo apt install gcc
Reading package lists... Done
Building dependency tree      
Reading state information... Done
gcc is already the newest version (4:7.3.0-3).
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

But when I run the program it does not find the installed version!

sudo apt install hplip && hp-setup

It just installs the defective drivers!

It just installed the defective drivers!

Solved! Uninstalled HPLIP through synaptic, restarted my notebook, installed HPLIP through terminal and finally I added manually the printer chosing " Network-driverless". I took 4 minutes to print but it worked! Thanks all for the suggestions!