Facing the same problem with an HP Spectre X360, I tested several distributions and several different kernel versions.
I also followed several guides explaining how the problem could be solved, but none worked for me. What I find curious is that in Ubuntu 19.10 and 20.04 in live mode the microphone works perfectly (both internal and the headset).
I copied the contents of the alsa-base.conf file from live and overwrote that of the distribution, but it also didn't work.
Tested with kernel: 5.0x, 5.3.x, 5.4.x, 5.5x (family 4.x bring other problems for my hardware)
I was also able to use an external microphone using a USB adapter.
Facing the same problem with an HP Spectre X360, I tested several distributions and several different kernel versions.
I also followed several guides explaining how the problem could be solved, but none worked for me. What I find curious is that in Ubuntu 19.10 and 20.04 in live mode the microphone works perfectly (both internal and the headset).
I copied the contents of the alsa-base.conf file from live and overwrote that of the distribution, but it also didn't work.
Tested with kernel: 5.0x, 5.3.x, 5.4.x, 5.5x (family 4.x bring other problems for my hardware)
I was also able to use an external microphone using a USB adapter.