Solve for a
\left\{\begin{matrix}a=\frac{3c}{-3\ln(b)+8\sinh(\frac{2}{3})r}\text{, }&r\neq \frac{3\ln(b)}{8\sinh(\frac{2}{3})}\text{ and }b>0\\a\in \mathrm{R}\text{, }&c=0\text{ and }r=\frac{3\ln(b)}{8\sinh(\frac{2}{3})}\text{ and }b>0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=e^{\frac{8\sinh(\frac{2}{3})r}{3}-\frac{c}{a}}\text{, }&a\neq 0\\b>0\text{, }&c=0\text{ and }a=0\end{matrix}\right.
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