Soldering the cables can be tricky...especially used ones as it is nearly impossible to get them perfectly clean on the inside. I acetone also and brake cleaner. I think the single most important thing (well the 2 most important things) are NOT TOO MUCH heat and GOOD FLUX. I use Staybrite silver solder with liquid flux and a small butane torch (the ones powered by a lighter inside if you know what I mean). Any small butane torch will do. Hold the cable upright in a vise leaving only about 2\" sticking out of the vise. Pour on liquid flux and heat the area below the tip of the cable...The solder should start feeding in the tip after the flux is bubbling. Do not heat the tip directly...gently heat just below it going around the cable. Direct heat will cause soot buildup on the cable and solder will not flow...I keep adding flux often. If a bead of solder forms, try dropping liquid flux on it while it's hot, it will most likely get it flowing. Once you got plenty in the tip, you can use a steel wool to clean the outside and flow some from the outside of the cable too...always gentle heat..if you heat it up red hot, you should throw it away right now as it will make the cable brittle and it will break at a later time.
Rudy did a good article on the subject a little while back:
www.modelgasboats.com/Magazine..._Soldering.html