What does this error mean HRESULT:0X80073712

These ones are typically caused by underlying problems on the PC that also often cause Windows Updates to fail to install. If we can fix the Windows Update trouble, we can usually get the iTunes trouble cleaned up en passant.

Go into your Windows update and try to check for new updates. If updates install, stock up on the ones you're behind on, restarting the PC if requested to do so. After the restart, try installing iTunes again. Does it go through this time for you?

If windows updates fail to install, go into your Update History and doubleclick the failures. What alphanumeric codes appear for you? Are they also 80073712, or some other number? (If they're another number, what number are you getting?)

This Error code is the error code I got when trying to install my windows updates.