Thank you for posting in Microsoft Q&A. For this question, HP, as the software vendor, may have more resources for troubleshooting. After researching from HP websites, someone suggest using the following commands for the silent installation. You may feel free to try it, and if the problem persists, suggest you contacting HP for better support.
Reg.exe ADD "HKLM\SOFTWARE\WOW6432Node\Hewlett-Packard\HPActiveSupport\HPSF" /v NotifyTray /t REG_SZ /d 0 /f
Reg.exe ADD "HKLM\SOFTWARE\WOW6432Node\Hewlett-Packard\HPActiveSupport\HPSF" /v NotifyPopup /t REG_SZ /d 0 /f
Reg.exe ADD "HKLM\SOFTWARE\WOW6432Node\Hewlett-Packard\HPActiveSupport\HPHC" /v Install /t REG_SZ /d 0 /f
msiexec /i hpsupportsolutionsframework.msi /qn
setup.exe /s /v /qn