How do I get this stuck faucet cartridge out without breaking everything?

That's a screw-in cartridge setup, and those mineral deposits are definitely what's fighting you. For an older wall-mounted brass valve like that, you aren't looking to pull it; you have to unthread the whole assembly. If you try to pull it straight out with pliers, you're just going to strip the internal housing or slip and damage the stem, wich usally leads to a much bigger headache behind the tile.

One trick that usually helps is to put the handle back on and **open the tap** all the way before you put a wrench on it. If the valve is closed, there's internal pressure and mechanical tension holding the stem against the seat. Opening it takes some of that stress off the threads. Since you've got heavy scale, you might want to spray some white vinegar or a dedicated lime remover on those threads and let it sit for twenty minutes. It won't work miracles, but it can soften the crust enough for your tool to get a solid bite on the brass. Don't bother with small pliers for the actual removal. You relly need a **socket wrench** (specifically a deep shower valve socket) or a large crescent wrench that fits perfectly. If it won't budge, try to tighten it just a hair first—maybe a sixteenth of a turn. That tiny bit of clockwise movement is often enough to crack the mineral seal. Once you feel that pop, it shold start backing out. Just take it slow and keep your wrench square so you don't round off the brass flats.

When you finally get that cartridge out, don't just shove a new one in. You need to look deep inside the valve body for the **faucet seat**. It’s the little brass ring at the very back that the cartridge washer seals against. If you leave an old, pitted seat in there, your brand new cartridge will start leaking again almost immediately. Use a seat tool to swap that out while you've got everything disassembled and you'll save yourself from doing this all over again in a month.

Wait, what exactly is a seat tool? I’ve never seen one of those at the hardware store. Is it like a specific size for diffrent brands, or is it a universal kind of deal? I’m looking at my own setup and I'm terrified of that clockwise movement you mentioned. If I accidentally over-tighten it and the pipe snaps inside the wall, am I basicly stuck? I'm wondering if there's a specific sound or feel I shoud listen for so I know I'm not about to break the whole manifold.

A seat tool is usally just a small, L-shaped or T-shaped bar with a square or hex head on the ends. Most hardware stores sell a universal one that covers 90% of brands. It's cheap insurance against a leak. As for snapping the pipe, if you’re relly leaning on it and the whole valve starts flexing behind the wall, back off. Try hitting the brass with a hair dryer or a heat gun for a few minutes. The heat helps expand the metal just enugh to break that mineral bond. I've saved plenty of old stems this way without needing to go full Hulk on the wrench. Just watch out for any plastic components nearby before you start.

If the heat gun doesn't do it, I've had luck giving the end of the wrench a few light taps with a rubber mallet. Sometimes that vibration breaks the crust loose better than a steady pull. Just don't go full Thor on it or you'll definately be opening up the wall. Also, when you're putting the new one back in, smear some waterproof plumber’s grease on the new threads. It prevents minerals from seizing it up again, so if you have to swap it in five years, it'll acutally come out without the workout. Those socket sets usally come with 5 or 6 sizes on a ring—just make sure you use the one that fits perfectly snug.

One detail often missed is checking for a retainer clip. If there is no hex nut shape on the cartridge body, look for a small U-shaped brass pin near the front. If that is there, no amount of unscrewing will help til it is pulled out with some needle-nose pliers. Once you get it out, spend five minutes cleaning the internal threads of the valve body with an old toothbrush and vinegar. If you try to thread a new brass cartridge into a body filled with calcified grit, you risk cross-threading it. I have had one seize halfway in beacuse of a tiny pebble of scale, and getting it back out without ruining the valve was a miracle.