Solve P=RT(1-C/Tv^3)

$$P = R T ( 1 - C / T v ^ { 3 } )$$

Solve for C

$$\left\{\begin{matrix}C=\frac{RT-P}{Rv^{3}}\text{, }&R\neq 0\text{ and }v\neq 0\text{ and }T\neq 0\\C\in \mathrm{R}\text{, }&\left(P=0\text{ and }R=0\text{ and }T\neq 0\right)\text{ or }\left(P=RT\text{ and }v=0\text{ and }T\neq 0\text{ and }R\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by T.

$$PT=RT\left(1-\frac{C}{T}v^{3}\right)T$$

Multiply T and T to get T^{2}.

$$PT=RT^{2}\left(1-\frac{C}{T}v^{3}\right)$$

Express \frac{C}{T}v^{3} as a single fraction.

$$PT=RT^{2}\left(1-\frac{Cv^{3}}{T}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{T}{T}.

$$PT=RT^{2}\left(\frac{T}{T}-\frac{Cv^{3}}{T}\right)$$

Since \frac{T}{T} and \frac{Cv^{3}}{T} have the same denominator, subtract them by subtracting their numerators.

$$PT=RT^{2}\times \frac{T-Cv^{3}}{T}$$

Express R\times \frac{T-Cv^{3}}{T} as a single fraction.

$$PT=\frac{R\left(T-Cv^{3}\right)}{T}T^{2}$$

Use the distributive property to multiply R by T-Cv^{3}.

$$PT=\frac{RT-RCv^{3}}{T}T^{2}$$

Express \frac{RT-RCv^{3}}{T}T^{2} as a single fraction.

$$PT=\frac{\left(RT-RCv^{3}\right)T^{2}}{T}$$

Cancel out T in both numerator and denominator.

$$PT=T\left(-CRv^{3}+RT\right)$$

Use the distributive property to multiply T by -CRv^{3}+RT.

$$PT=-TCRv^{3}+RT^{2}$$

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

$$-TCRv^{3}+RT^{2}=PT$$

Subtract RT^{2} from both sides.

$$-TCRv^{3}=PT-RT^{2}$$

Reorder the terms.

$$-CRTv^{3}=PT-RT^{2}$$

The equation is in standard form.

$$\left(-RTv^{3}\right)C=PT-RT^{2}$$

Divide both sides by -RTv^{3}.

$$\frac{\left(-RTv^{3}\right)C}{-RTv^{3}}=\frac{T\left(P-RT\right)}{-RTv^{3}}$$

Dividing by -RTv^{3} undoes the multiplication by -RTv^{3}.

$$C=\frac{T\left(P-RT\right)}{-RTv^{3}}$$

Divide T\left(P-RT\right) by -RTv^{3}.

$$C=-\frac{P-RT}{Rv^{3}}$$

Solve for P

$$P=R\left(T-Cv^{3}\right)$$

$$T\neq 0$$