You can put this solution on YOUR website! First of all, I rewrote your equation so that the c stays in the numerator instead of the denominator. I think you really meant it that way. I assume that you're beginning Algebra, and making you solve for a variable that's in the denominator is a bit advanced for this time of the year.
The technique here is to find the GCF of the denominators, and multiply EVERY term by that GCF. That's supposed to get rid of the denominator so that your equation will no longer involve fractions.
I know that your teacher will not be happy with the idea of the "lazy GCF". The lazy GCF is simply obtained taking all terms in the denominator and multiplying them together. In this case, the terms are 10 and 5. The lazy GCF would then be 10*5 which really is 50. We would then multiply EVERY term by 50:
<------ start here.
<---- multiply all terms by the lazy GCF, which is 50.
<---- You'll see that the denominators will cancel and you'll end up with this linear equation.
<---- add 500 to both sides
<----- Divide both sides by 35. Numerically, c is approximately 14.857, or 104/7 in improper fraction form in lowest terms.
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