How to clean extreme carpet dirt?

I use homemade laundry soap to scrub mine. I sometimes add a scoop of oxy clean. I'd recommend renting a carpet scrubber if you don't have one. They are about $30 for 24 hours. If the stains are really bad, pretreat with Shout or something like that and then scrub.

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Shiny dirty? As in the pile is compacted flat and the dirt has oily residues in it? It’s time for replacing the carpet with peel and stick vinyl tile, IMO.

If your time is worth absolutely nothing, then I’d say, work on getting the pile uncompacted first. One can’t clean it when compacted.

If the carpet has soapy residues in it from cleanings years ago, then keep in mind that more soap is not the answer. Steam extraction, maybe.

I would not saturate the carpet because the pad will hold the water. That can lead to mold and damage to the subfloor.

Unfortunately, the carpet has run it's time out. You really need to pull that germ-ridden filth from the place where people are living. Even if you end up putting poly over a subfloor it will be a better environment to live in!