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To clean an office cubicle, treat it in a similar fashion to upholstery. First, vacuum it regularly to avoid dust and dirt from getting ground in. Try the following in a non-visible area first, to ensure that the fabric is color-fast. Mix 1/4 cup high-suds laundry detergent with one quart of warm water. (If you can, do this in a blender or with a mixer to make the most suds possible.) Apply just the suds with a medium-bristled brush. Work lather in small circles, overlapping as your go. Wring out a towel in clean water and go over the entire surface. Be careful not to get the fabric too wet at any time. When dry, vacuum to remove any remaining residue.
I don't think this is a good idea. It's too hard to get out all the soap residue. The soap residue will act like a dirt magnet. Your upholstery will never be the same. It's better to spray on a solution of 1 part white vinegar, 6 parts water. Then sponge up excess with clean dry towel & allow to air dry.