Print quality issues usually boil down to a few common areas:
- HP vs 3rd party toner cartridges
- Paper quality
- Application settings
- Driver settings
- Color profiling
The first step is to confirm if you are using HP original cartridges or not. If not then you need to work with your 3rd party reseller on print quality issues. It sounds silly, but the printers are only calibrated for OEM cartridges when color quality issues arrise. 3rd party can often do a passable job, but artists and designers like yourself will notice the difference in certain situations where color quality is important.
After that you will want to verify the quality of the paper you are printing on. A mismatch of the paper settings can account for variations in print quality. The printer needs to understand what is loaded in the trays so that it can adjust the heat and electrical charges used to attract the toner to the paper. Perhaps all you have to do is tell teh printer you are printing on "glossy" paper instead of plain.
Application settings are where things get tricky. Design heavy applications like Photoshop and Indesign are highly adjustable and customizable compared to a more simple application like Windows Photo Gallery. Try printing a diagnostic or demonstration page directly from the control panel of the printer to confirm if the quality issues are application specific or something on the printer. If the printer prints fine from the control panel then try printing from a few different applications to compare and see if the issue is isolated to your Adobe products or not. Consult Adobe if it is for color profiling options.
Driver settings, or rather the driver language used to send print jobs to the printer. A simple swap from PCL6 to PostScript can have a big impact on your output as some print languages are better able to handle high design print jobs than others. Feel free to dabble in the various model specific drivers HP offers on thier Support Site. Your printer is also compatible with HP Universal Print Drivers if you care to venture out that way and experiment too.
Finally, there is good old fashioned ICC Color Profiles. This one takes some trial and error. In a nutshell, it is a configuration process that helps you calibrate what you see on your screen to what is physically printed from the printer. Lots of info out there on ICC color profiling with a quick Google search.