Solve R=R_{0}(1+at)

$$R = R _ { 0 } ( 1 + a t )$$

Solve for R_0

$$\left\{\begin{matrix}R_{0}=\frac{R}{at+1}\text{, }&t=0\text{ or }a\neq -\frac{1}{t}\\R_{0}\in \mathrm{R}\text{, }&R=0\text{ and }a=-\frac{1}{t}\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply R_{0} by 1+at.

$$R=R_{0}+R_{0}at$$

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

$$R_{0}+R_{0}at=R$$

Combine all terms containing R_{0}.

$$\left(1+at\right)R_{0}=R$$

The equation is in standard form.

$$\left(at+1\right)R_{0}=R$$

Divide both sides by 1+at.

$$\frac{\left(at+1\right)R_{0}}{at+1}=\frac{R}{at+1}$$

Dividing by 1+at undoes the multiplication by 1+at.

$$R_{0}=\frac{R}{at+1}$$

Solve for R

$$R=R_{0}\left(at+1\right)$$