Solve Q=1/3mct*tanm

$$Q = \frac { 1 } { 3 } m c t \times \tan m$$

Solve for c

$$\left\{\begin{matrix}c=\frac{3Q\cot(m)}{mt}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\left(m>\frac{\pi n_{1}}{2}\text{ and }m<\frac{\pi n_{1}}{2}+\frac{\pi }{2}\right)\text{ and }t\neq 0\\c\in \mathrm{R}\text{, }&\left(Q=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }m=\pi n_{2}\right)\text{ or }\left(Q=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }m=\pi n_{1}+\frac{\pi }{2}\text{ and }t=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{3}mct\tan(m)=Q$$

The equation is in standard form.

$$\frac{mt\tan(m)}{3}c=Q$$

Divide both sides by \frac{1}{3}mt\tan(m).

$$\frac{3\times \frac{mt\tan(m)}{3}c}{mt\tan(m)}=\frac{3Q}{mt\tan(m)}$$

Dividing by \frac{1}{3}mt\tan(m) undoes the multiplication by \frac{1}{3}mt\tan(m).

$$c=\frac{3Q}{mt\tan(m)}$$

Divide Q by \frac{1}{3}mt\tan(m).

$$c=\frac{3Q\cot(m)}{mt}$$

Solve for Q

$$Q=\frac{cmt\tan(m)}{3}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }m=\pi n_{1}+\frac{\pi }{2}$$