Solve y=mc^2x

$$y = m c ^ { 2 } x$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{y}{xc^{2}}\text{, }&x\neq 0\text{ and }c\neq 0\\m\in \mathrm{C}\text{, }&\left(x=0\text{ or }c=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mc^{2}x=y$$

The equation is in standard form.

$$xc^{2}m=y$$

Divide both sides by c^{2}x.

$$\frac{xc^{2}m}{xc^{2}}=\frac{y}{xc^{2}}$$

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

$$m=\frac{y}{xc^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{y}{xc^{2}}\text{, }&x\neq 0\text{ and }c\neq 0\\m\in \mathrm{R}\text{, }&\left(x=0\text{ or }c=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mc^{2}x=y$$

The equation is in standard form.

$$xc^{2}m=y$$

Divide both sides by c^{2}x.

$$\frac{xc^{2}m}{xc^{2}}=\frac{y}{xc^{2}}$$

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

$$m=\frac{y}{xc^{2}}$$

Solve for c (complex solution)

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

Solve for c

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