d. \( r=\frac{C}{2 r}+2 r+2 L \quad \) is \( r \) isolated?

To isolate \( r \) in the equation \( r = \frac{C}{2r} + 2r + 2L \), you'll want to first move all terms involving \( r \) to one side. Subtract \( 2r \) from both sides and multiply through by \( 2r \) to eliminate the fraction, leading to a polynomial equation. Solving this will help you isolate \( r \). Watch out for potential complications, such as quadratic terms! When dealing with equations like this, common mistakes include mismanaging the distributive properties or forgetting to adjust each term when moving them. Always double-check your operations and be cautious with your signs. A little care goes a long way when isolating variables in equations!