Even if you are not able to soak up the wine in time, most of the stain will disappear when you clean the fabric thoroughly with soap and water.
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Use a lint-free towel to blot up as much of the red wine as possible when the spill occurs. If you do not do this, the stain will become more difficult to remove later.
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Pour salt on the spill to absorb more of the wine. Let the salt rest on the stain while you prepare a mixture of 1 tablespoon laundry soap in a bowl of hot water. Brush or vacuum the salt off the stain.
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Soak a towel in the soapy water, and squeeze out excess water. Dab the red wine with the towel. Rinse the towel as necessary, and repeat until the towel stops lifting the red wine.