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Remove the offending piece of furniture from the carpet before cleaning. Scrape up excess rust with a butter knife. Apply lemon juice and salt directly onto the stained area. Pour 2 cups (470 mL) of hot water onto the treated carpet. Use a clean white towel to blot up the excess liquid. Use a mixture of lemon juice, white vinegar, and salt for tougher stains.
You’ll want to either find a new location for that piece of furniture or look into coating it with an anti-rust solution to prevent new stains.  Check your windows—leaky windows can let in extra moisture that then reacts with the metal in your furniture to cause rust. The more rust you can remove before cleaning, the better your chances of getting rid of the stain completely. Be patient and gentle as you scrape—you want to be thorough but you also don’t want to rip or snag the carpet threads. Vacuum up the flaked rust from the carpet before moving on to the stain removal steps. You can use fresh lemon juice or bottled—whichever you have on hand will work! If you have sea salt, sprinkle that on top of the lemon-soaked area. If you don’t have sea salt, common table salt will work, too. Let the stain soak for 5 minutes.  The lemon juice and salt combination creates a mild abrasive cleaner and helps break up the rust composition.  If you like a more hands-on approach, you can mix the lemon juice and salt in a bowl and use a sponge to blot it onto the stain directly. The rust stain should start to disappear. If the stain is particularly large, you may need to use more than 2 cups (470 mL) of hot water. The main thing to keep in mind is that you want the water to saturate the stain so it removes the salt and lemon juice mixture and clears the stain. Try to get as much of it soaked up from the carpet as you can. If the towel you’re using gets completely soaked, use another clean white towel and continue until the area is as dry as possible. Allow the area to dry completely before placing any furniture back on it. Mix 1 cup (240 mL) of white vinegar with 2 tablespoons (30 mL) of lemon juice and 1 tablespoon (15 mL) of salt. Pour this mixture onto the stain and let it sit for 2 hours. After a few hours have passed, blot the area with a damp white towel until it comes clean.