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I see from the post that you are getting an error message "Print Cartridge Problem" on your HP Photosmart printer. Don't worry I'll try my best to help you with this,
To provide you with an accurate solution, I'll need a few more details:
Have you recently made any changes on the printer before the issue started?
Are you using genuine HP Ink cartridges or refilled cartridges?
Have you tried to clean the cartridge contacts and rollers?
In the meantime, let's start off by performing a Hard reset on the printer and make sure that the printer is connected directly to the wall outlet and not to the surge protector.
Remove all the ink cartridges and then try to perform a hard reset on the printer.
With the printer turned on, disconnect the power cord from the rear of the printer and also unplug the power cord from the wall outlet.
Remove USB cable, if present.
Wait for 2-3 minutes, press and hold the power button on your printer for about 30 seconds to remove any additional charge.
Now plug back the power cable straight to a wall outlet without any surge protector or an extension cord and then plug back the power cord to the printer.
Turn on the printer and wait till warm-up period finishes and the printer is idle.
Now insert the ink cartridges and then try to print a test page and check if it works.
Let’s first try and make a “photocopy” to determine whether the issue is with the printer or not. Place a document on the scanner glass and choose “Copy” option. If the printer is making a good copy, then the printer hardware is fine.
Please attempt these steps here:
Remove, inspect, and then reinstall the cartridges
Clean the cartridge and carriage electrical contacts