Solve n/R_{200}=a+bT+cT

$$\frac { n } { R _ { 200 } } = a + b T + c T$$

Solve for R_200

$$\left\{\begin{matrix}R_{200}=\frac{n}{Tb+Tc+a}\text{, }&n\neq 0\text{ and }a\neq -T\left(b+c\right)\\R_{200}\neq 0\text{, }&a=-T\left(b+c\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable R_{200} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R_{200}.

$$n=R_{200}a+bTR_{200}+cTR_{200}$$

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

$$R_{200}a+bTR_{200}+cTR_{200}=n$$

Combine all terms containing R_{200}.

$$\left(a+bT+cT\right)R_{200}=n$$

The equation is in standard form.

$$\left(Tb+Tc+a\right)R_{200}=n$$

Divide both sides by a+bT+Tc.

$$\frac{\left(Tb+Tc+a\right)R_{200}}{Tb+Tc+a}=\frac{n}{Tb+Tc+a}$$

Dividing by a+bT+Tc undoes the multiplication by a+bT+Tc.

$$R_{200}=\frac{n}{Tb+Tc+a}$$

Variable R_{200} cannot be equal to 0.

$$R_{200}=\frac{n}{Tb+Tc+a}\text{, }R_{200}\neq 0$$

Solve for T

$$\left\{\begin{matrix}T=-\frac{R_{200}a-n}{R_{200}\left(b+c\right)}\text{, }&b\neq -c\text{ and }R_{200}\neq 0\\T\in \mathrm{R}\text{, }&n=R_{200}a\text{ and }b=-c\text{ and }R_{200}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{200}.

$$n=R_{200}a+bTR_{200}+cTR_{200}$$

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

$$R_{200}a+bTR_{200}+cTR_{200}=n$$

Subtract R_{200}a from both sides.

$$bTR_{200}+cTR_{200}=n-R_{200}a$$

Combine all terms containing T.

$$\left(bR_{200}+cR_{200}\right)T=n-R_{200}a$$

The equation is in standard form.

$$\left(R_{200}b+R_{200}c\right)T=n-R_{200}a$$

Divide both sides by cR_{200}+bR_{200}.

$$\frac{\left(R_{200}b+R_{200}c\right)T}{R_{200}b+R_{200}c}=\frac{n-R_{200}a}{R_{200}b+R_{200}c}$$

Dividing by cR_{200}+bR_{200} undoes the multiplication by cR_{200}+bR_{200}.

$$T=\frac{n-R_{200}a}{R_{200}b+R_{200}c}$$

Divide n-R_{200}a by cR_{200}+bR_{200}.

$$T=\frac{n-R_{200}a}{R_{200}\left(b+c\right)}$$