Fatal mistake, the way you are factoring the exponential pieces. You can not factor the 5 out like that, or the 1 like that.
I came to the same conclusion today while at school, this problem has been bugging me for 24 hours. Me and 4 other grad students worked on it over lunch to no avail, no way the problem posted as is should be assigned in a pre calculus class, maybe a numerical methods course at best.
If it is as Mr. Fantastic suggested (and I hope it is) simply substitute and solve the quadratic to see how he got his factoring, then you are basically done.