I am going to make an assumption here that something happened between the time you bought your car and now. Credit card debt at 25 percent interest and a credit score of 660 does not fit with the phrase "lots of equity in my car." Generally speaking, most people who have car loans have little or no equity in their vehicles simply because cars depreciate in value so quickly. The fact that you have lots of equity means you probably made a fairly substantial down payment, or perhaps paid cash for your car. So my guess is that your finances were fat in the past but are thinner now.
The reason I say this is relevant to my answer. If something did already happen that negatively affected your finances (decreased hours at work, divorce, bad run in Vegas, etc.), there's always the chance the bad news isn't over. And if it's not, you may need the opportunity to refinance your vehicle or just sell the car and trade down to get some cash for something more important than paying off credit card debt -- like paying rent or buying food.
The other consideration I want you to think about is that by refinancing the car to pay off your credit cards, you are changing unsecured debt into secured debt and as a result, possibly putting your car at risk. Fall behind on credit card debt, and you get nasty phone calls. Fall behind on your car payment, and you get to walk to work. And if you can't walk that far, you get to collect a meager unemployment check. So while I like your overall goal, I believe you can come up with a better solution.
You might consider a personal loan from your credit union. Credit unions tend to be more forgiving when making loans to their members than banks. With a credit score of 660, you may need some forgiveness. If you qualify for a car loan with 6 percent to 7 percent interest, you may qualify for a personal loan with a better interest rate than the 25 percent you are paying on your cards. You would be saving money with a lower interest rate and would stay with an unsecured loan and keep your car out of jeopardy. Another alternative is to aggressively pay down the credit card balances. If you can come up with $320 per month for the card payments, it would take you two years to pay off your current balances, even with your high interest rate.
Whatever you ultimately decide to do to pay off your credit card balances, you need to be committed to not adding any additional charges to your balances. The only way I know of to do this is to start saving. I want you to have money in an emergency savings account for those unexpected happenings that are sure to come up when you can least afford them. Your next goal should be to save six months' to a year's worth of living expenses in an emergency fund. If you don't, you'll always be behind the financial eight ball.
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