Solve T=alpha+betaR/R_{300}+gamma(R/R_{300})

$$T = \alpha + \beta \frac { R } { R _ { 300 } } + \gamma ( \frac { R } { R _ { 300 } } )$$

Solve for R

$$\left\{\begin{matrix}R=\frac{R_{300}\left(T-\alpha \right)}{\beta +\gamma }\text{, }&\beta \neq -\gamma \text{ and }R_{300}\neq 0\\R\in \mathrm{R}\text{, }&T=\alpha \text{ and }\beta =-\gamma \text{ and }R_{300}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{300}.

$$TR_{300}=R_{300}\alpha +\beta R+\gamma R$$

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

$$R_{300}\alpha +\beta R+\gamma R=TR_{300}$$

Subtract R_{300}\alpha from both sides.

$$\beta R+\gamma R=TR_{300}-R_{300}\alpha$$

Combine all terms containing R.

$$\left(\beta +\gamma \right)R=TR_{300}-R_{300}\alpha$$

The equation is in standard form.

$$\left(\beta +\gamma \right)R=R_{300}T-R_{300}\alpha$$

Divide both sides by \beta +\gamma .

$$\frac{\left(\beta +\gamma \right)R}{\beta +\gamma }=\frac{R_{300}\left(T-\alpha \right)}{\beta +\gamma }$$

Dividing by \beta +\gamma undoes the multiplication by \beta +\gamma .

$$R=\frac{R_{300}\left(T-\alpha \right)}{\beta +\gamma }$$

Solve for R_300

$$\left\{\begin{matrix}R_{300}=-\frac{R\left(\beta +\gamma \right)}{\alpha -T}\text{, }&\beta \neq -\gamma \text{ and }R\neq 0\text{ and }T\neq \alpha \\R_{300}\neq 0\text{, }&T=\alpha \text{ and }\left(\beta =-\gamma \text{ or }R=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable R_{300} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R_{300}.

$$TR_{300}=R_{300}\alpha +\beta R+\gamma R$$

Subtract R_{300}\alpha from both sides.

$$TR_{300}-R_{300}\alpha =\beta R+\gamma R$$

Combine all terms containing R_{300}.

$$\left(T-\alpha \right)R_{300}=\beta R+\gamma R$$

The equation is in standard form.

$$\left(T-\alpha \right)R_{300}=R\beta +R\gamma$$

Divide both sides by T-\alpha .

$$\frac{\left(T-\alpha \right)R_{300}}{T-\alpha }=\frac{R\left(\beta +\gamma \right)}{T-\alpha }$$

Dividing by T-\alpha undoes the multiplication by T-\alpha .

$$R_{300}=\frac{R\left(\beta +\gamma \right)}{T-\alpha }$$

Variable R_{300} cannot be equal to 0.

$$R_{300}=\frac{R\left(\beta +\gamma \right)}{T-\alpha }\text{, }R_{300}\neq 0$$