Solve varepsilon=MC^2

$$\varepsilon = M C ^ { 2 }$$

Solve for M (complex solution)

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

Steps for Solving Linear Equation

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

$$MC^{2}=\epsilon$$

The equation is in standard form.

$$C^{2}M=\epsilon$$

Divide both sides by C^{2}.

$$\frac{C^{2}M}{C^{2}}=\frac{\epsilon }{C^{2}}$$

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

$$M=\frac{\epsilon }{C^{2}}$$

Solve for M

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

Steps for Solving Linear Equation

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

$$MC^{2}=\epsilon$$

The equation is in standard form.

$$C^{2}M=\epsilon$$

Divide both sides by C^{2}.

$$\frac{C^{2}M}{C^{2}}=\frac{\epsilon }{C^{2}}$$

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

$$M=\frac{\epsilon }{C^{2}}$$

Solve for C (complex solution)

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

Solve for C

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