Take heart. This is a little messy, but you can do it. You're not going to get any of the variables alone in an equation right away. Don't be stopped by that. It doesn't mean you can't solve the problem. It just means you have to be content to work with combinations of variables for a while.
You can start a problem like this by finding, say, two expressions for the quantity (B+C), and setting them equal to each other. You can use this result to find two expressions for, say, the quantity (B*C), and set them equal to each other. Make sure you're using all three equations, otherwise, you'll end up demonstrating something like A=A -- true, but not useful.
Eventually, you will need the quadratic equation. Either root will work; there are at least two solutions. (There should be more; I'm too lazy to work out how many.)
You can get cubic equations in one variable from this problem. I don't remember how to solve those guys, but I was able to factor the one I got, and just guess an answer to it.
Good luck. Check your work frequently, so you don't start feeling like you might be just propagating a mistake. Try to enjoy yourself. The feeling of power you can get from solving a problem like this can make it worth great effort, even though you might not care at all what the answer is.
