Solve m=frac{k_{B}T}{sigmaOmega}

$$m = \frac { k _ { B } T } { \sigma \Omega }$$

Solve for T

$$\left\{\begin{matrix}T=\frac{m\Omega \sigma }{k_{B}}\text{, }&k_{B}\neq 0\text{ and }\sigma \neq 0\text{ and }\Omega \neq 0\\T\in \mathrm{R}\text{, }&m=0\text{ and }k_{B}=0\text{ and }\sigma \neq 0\text{ and }\Omega \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \Omega \sigma .

$$m\Omega \sigma =k_{B}T$$

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

$$k_{B}T=m\Omega \sigma$$

Divide both sides by k_{B}.

$$\frac{k_{B}T}{k_{B}}=\frac{m\Omega \sigma }{k_{B}}$$

Dividing by k_{B} undoes the multiplication by k_{B}.

$$T=\frac{m\Omega \sigma }{k_{B}}$$

Solve for k_B

$$\left\{\begin{matrix}k_{B}=\frac{m\Omega \sigma }{T}\text{, }&T\neq 0\text{ and }\sigma \neq 0\text{ and }\Omega \neq 0\\k_{B}\in \mathrm{R}\text{, }&m=0\text{ and }T=0\text{ and }\sigma \neq 0\text{ and }\Omega \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \Omega \sigma .

$$m\Omega \sigma =k_{B}T$$

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

$$k_{B}T=m\Omega \sigma$$

The equation is in standard form.

$$Tk_{B}=m\Omega \sigma$$

Divide both sides by T.

$$\frac{Tk_{B}}{T}=\frac{m\Omega \sigma }{T}$$

Dividing by T undoes the multiplication by T.

$$k_{B}=\frac{m\Omega \sigma }{T}$$