It was going to bed time when I posted - Zorin should include HPLIP - if not, after post-install update the system, then from Software channel install Synaptic Package Manager. Just be aware that if this is for ZorinOS 15 you should avoid the 'Zorin on Wayland' like the plague. Synaptic will not run if you are using Zorin on Wayland. Once Synaptic is installed, search for HP LIP (having checked the Linux driver page, that model of printer is supported). Just compare the version of HPLIP available via Synaptic and see if it is the same version as that given from the download. It will be a .deb package - please be sure that you choose the correct version as there is apparently 32-bit and 64-bit versions.
[Footnote: Wayland should have been consigned to the Software Recycle Bin at point of concept in much the same way Chrome Books and MMe notebooks should have been consigned to the hardware recycle bin!]