Solve varepsilon_{c}=mc^2

$$\varepsilon _ { c } = m c ^ { 2 }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\epsilon _{c}}{c^{2}}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&\epsilon _{c}=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mc^{2}=\epsilon _{c}$$

The equation is in standard form.

$$c^{2}m=\epsilon _{c}$$

Divide both sides by c^{2}.

$$\frac{c^{2}m}{c^{2}}=\frac{\epsilon _{c}}{c^{2}}$$

Dividing by c^{2} undoes the multiplication by c^{2}.

$$m=\frac{\epsilon _{c}}{c^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\epsilon _{c}}{c^{2}}\text{, }&c\neq 0\\m\in \mathrm{R}\text{, }&\epsilon _{c}=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mc^{2}=\epsilon _{c}$$

The equation is in standard form.

$$c^{2}m=\epsilon _{c}$$

Divide both sides by c^{2}.

$$\frac{c^{2}m}{c^{2}}=\frac{\epsilon _{c}}{c^{2}}$$

Dividing by c^{2} undoes the multiplication by c^{2}.

$$m=\frac{\epsilon _{c}}{c^{2}}$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-m^{-\frac{1}{2}}\sqrt{\epsilon _{c}}\text{; }c=m^{-\frac{1}{2}}\sqrt{\epsilon _{c}}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&\epsilon _{c}=0\text{ and }m=0\end{matrix}\right.$$

Solve for c

$$\left\{\begin{matrix}c=\sqrt{\frac{\epsilon _{c}}{m}}\text{; }c=-\sqrt{\frac{\epsilon _{c}}{m}}\text{, }&\left(\epsilon _{c}\geq 0\text{ and }m>0\right)\text{ or }\left(\epsilon _{c}\leq 0\text{ and }m<0\right)\\c\in \mathrm{R}\text{, }&\epsilon _{c}=0\text{ and }m=0\end{matrix}\right.$$