Solve y=1/2mc^2

$$y = 1 / 2 m c ^ { 2 }$$

Solve for m (complex solution)

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

Steps for Solving Linear Equation

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

$$\frac{1}{2}mc^{2}=y$$

The equation is in standard form.

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

Divide both sides by \frac{1}{2}c^{2}.

$$\frac{2\times \frac{c^{2}}{2}m}{c^{2}}=\frac{2y}{c^{2}}$$

Dividing by \frac{1}{2}c^{2} undoes the multiplication by \frac{1}{2}c^{2}.

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

Solve for m

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

Steps for Solving Linear Equation

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

$$\frac{1}{2}mc^{2}=y$$

The equation is in standard form.

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

Divide both sides by \frac{1}{2}c^{2}.

$$\frac{2\times \frac{c^{2}}{2}m}{c^{2}}=\frac{2y}{c^{2}}$$

Dividing by \frac{1}{2}c^{2} undoes the multiplication by \frac{1}{2}c^{2}.

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

Solve for c (complex solution)

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

Solve for c

$$\left\{\begin{matrix}c=\sqrt{\frac{2y}{m}}\text{; }c=-\sqrt{\frac{2y}{m}}\text{, }&\left(y\geq 0\text{ and }m>0\right)\text{ or }\left(y\leq 0\text{ and }m<0\right)\\c\in \mathrm{R}\text{, }&y=0\text{ and }m=0\end{matrix}\right.$$