Rub in baking soda with a damp sponge or plastic scrubber sponge and rinse with fresh water. For tougher jobs, wipe surfaces with vinegar first and follow with baking soda as a scouring powder. (Vinegar can break down tile grout, so use sparingly.)
You might want to get a steam cleaner. Mine is the Euro-ProX and it's worth it's weight in gold! I've cleaned spots out of the carpet that had been there for years before I finally got the idea to try this. I'm sure it'd work on those grout problems you have.
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