Solving equation and plotting issue with Mathematica

[djymndl07]

I have a function $f(\text{r})\text{=}-\frac{a Q^4}{20 r^6}-\frac{c}{r^{3 \omega +1}}-\frac{2 M}{r}+\frac{8}{3} \pi P r^2+\frac{Q^2}{r^2}+1;$ and an expression $$\text{Tinv2}=\frac{2^{2/3} \pi ^{4/3} a Q^4}{9 \sqrt[3]{3} V^{7/3}}+c 2^{2 \omega -\frac{2}{3}} \left(\frac{3}{\pi }\right)^{\frac{1}{3}-\omega } \omega V^{-\omega -\frac{2}{3}}+\sqrt[3]{\frac{6}{\pi }} P \sqrt[3]{V}-\frac{Q^2}{3 V}+\frac{1}{2 \sqrt[3]{6} \pi ^{2/3} \sqrt[3]{V}};$$. Now I want to solve r from $$-5 a Q^4-6 c \omega (3 \omega +5) r^{5-3 \omega }-4 r^4 \left(8 \pi P-3 Q^2+2 r^2\right)=0$$ and use it to obtain plot for Tinv2. Then I want to solve for r from $f(r)=0$ and use it to plot another function. Now I am getting error and obtained no plots. Can any one tell me where am I doing mistake and how can I fix it? Please follow the link here for the detailed question and notebook.