1. The problem statement, all variables and given/known data I have to reverse engineer a derivation in a paper and have no idea where to even start. The amount of terms are overwhelming and I can't imagine how the author even began. 2. Relevant equations The following equations are known: http://img7.imagebanana.com/img/jpfqw5qj/Selection_001.png http://img7.imagebanana.com/img/v4cx2e07/Selection_009.png http://img6.imagebanana.com/img/ape27n0j/Selection_002.png Substituting them into the following equation gives an expression where [itex]r[/itex] needs to be isolated. http://img6.imagebanana.com/img/gayq1jb5/Selection_008.png The author makes many substitutions and results in the following simplified equation. http://img6.imagebanana.com/img/5gmnl628/Selection_007.png The substitutions are as follows: http://img6.imagebanana.com/img/36qfovp8/Selection_004.png http://img6.imagebanana.com/img/iinwallf/Selection_005.png http://img7.imagebanana.com/img/japtx4e8/Selection_006.png What I'm trying to do is figure out how he arrived at these coefficients [a], , [c], V, etc. 3. The attempt at a solution I've substituted (1)--(5) into (6) but don't know where to go from here. The equation is huge and has many terms. I'm not sure how/where to begin. Any help will be much appreciated. Thanks.