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@vu2nan The two corresponding jacks on my laptop. I just plugged them into where they should've gone. The speaker works perfectly. The mic works too, but it's too noisy. So, they are connected to the right ports - if that's what you mean.
I tried using a multimeter to check for available shortcircuits but found none. However, I guess my computer is making the loop somehow, maybe it has a common ground right? That has made me suspicious because for getting a more clear sound from the microphone, is only possible when BOTH mic and headset are connected to the same computer.