can not install a hp 3510e printer

Have you installed HPLIP Toolbox from Ubuntu Software Center?

What is the output of :

lsb_release -a; uname -a

Thanks

Please read this:

http://hplipopensource.com/hplip-web/models/deskjet_aio/deskjet_3510_series.html

So your printer needs a minimum hplip version of 3.12.9

However, read this as well:

http://packages.ubuntu.com/search?keywords=hplip

It shows that all official versions of Ubuntu do not includes versions 3.12.9 or higher of hplip (except for raring, which is NOT released and not ready yet).

So you cannot install hplip 3.12.6 using the apt-get package manager. That version is too old.

So you need to download and install hplip 3.13.3 from here:

http://hplipopensource.com/hplip-web/downloads.html
http://prdownloads.sourceforge.net/hplip/hplip-3.13.3.run

1) Run the following command in a Terminal:

sudo hp-uninstall

2)Follow installation instructions provided at:

    http://hplipopensource.com/hplip-web/install/install/index.html

3) Reconfigure print queue with the commands in the terminal mentioned below.
       => system-config-printer (remove all print queues)
      => sudo hp-plugin (This will download right plugin)
       => hp-setup (It should not be run in a root mode. This command is adding print queue, make sure you select ppd name having "-ps" or "hpcups" substring)
=>Try printing now.

Sources:
https://answers.launchpad.net/hplip/+question/214021
http://hplipopensource.com/hplip-web/models/deskjet_aio/deskjet_3510_series.html
http://packages.ubuntu.com/search?keywords=hplip
http://hplipopensource.com/hplip-web/downloads.html
http://prdownloads.sourceforge.net/hplip/hplip-3.13.3.run