Solve varepsilon=3/2kT

$$\varepsilon = \frac { 3 } { 2 } k T$$

Solve for T

$$\left\{\begin{matrix}T=\frac{2\epsilon }{3k}\text{, }&k\neq 0\\T\in \mathrm{R}\text{, }&\epsilon =0\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{3}{2}kT=\epsilon$$

The equation is in standard form.

$$\frac{3k}{2}T=\epsilon$$

Divide both sides by \frac{3}{2}k.

$$\frac{2\times \frac{3k}{2}T}{3k}=\frac{2\epsilon }{3k}$$

Dividing by \frac{3}{2}k undoes the multiplication by \frac{3}{2}k.

$$T=\frac{2\epsilon }{3k}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{2\epsilon }{3T}\text{, }&T\neq 0\\k\in \mathrm{R}\text{, }&\epsilon =0\text{ and }T=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{3}{2}kT=\epsilon$$

The equation is in standard form.

$$\frac{3T}{2}k=\epsilon$$

Divide both sides by \frac{3}{2}T.

$$\frac{2\times \frac{3T}{2}k}{3T}=\frac{2\epsilon }{3T}$$

Dividing by \frac{3}{2}T undoes the multiplication by \frac{3}{2}T.

$$k=\frac{2\epsilon }{3T}$$