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@NRB525 - Applman's math is fairly close assuming the OP would pay the entire balance off in a year or so. A much more realistic scenario is the OP refis their mortgage with a new 30 year term. They take out enough equity to pay off the entire CC debt plus a little extra to rebuild their emergency fund. The OP will probably not get the best interest rate due to their credit score and not wanting to pay closing cost out of pocket. Even so, the interest rate will be much lower. Obviously, since the interest rate is so much lower, they will save money. The OP will not appreciate us trying to prove otherwise.
I'd take a two step approach OP and I don't know how this works so you'll need to do some research: HELOC's and HEL's are at bargain basement rates too along with mortgages: I'd go get what amounts to the second mortgage HEL, pay off my revolving debt, then go refinance the whole enchilada after six months if it were possible... I'd really look into that before I tried non-trivial non-secured installment debt, or a bunch of random BT's or whatever.
You were planning to leverage the asset anyway, use it to help you accomplish the first step and get you quickly to a place where you can do the second step potentially: just do a bit of research on the HEL -> Refi two-step, I'm sure it's possible I just don't have the specifics. Make friends with a quality credit union in your local area regarding the HEL, and socialize the refinance of primary and secondary mortgage deal with a LO at your lender of choice would be my recommendation.
Alternatively look into a FHA or this new Bank of America refinance or similar program where you might be close to the credit score right now.