c^2 -81/c^2 +12c-27=0 Multiply everything by c^2. c^4 -81+12c^3-27c^2=0 You will now have to do the rational roots test. It will take a while to explain, which unfortunately there is not enough time to do so here. Check: http://www.purplemath.com/modules/solvpoly.htm For an explanation on how to do the rational root test. Lets rewrite it in a more easy way to work with: c^4+12c^3-27c^2-81=0 The factors of 81 are 3^4 so lets try c=3 and c=-3 as roots c=3 works as a root! when we plug it in we get 324-324=0 c=-3 45-243-81=NOT 0 So c=3 is a root. Lets simplify... Use long division to factor the original polynomial with (c-3). Using graphical methods you can find a root exists at c=15. Taken together we see:

(c-3)(c+15)(c^2+18 +(-216c +729)/(c-3)(c+15)))

Given this, I probably mistook the problem you meant. Post the correct problem and I can solve it.