Solve R=p+q(m_{0}d_{2})

$$R = p + q ( m _ { 0 } d _ { 2 } )$$

Solve for d_2

$$\left\{\begin{matrix}d_{2}=-\frac{p-R}{m_{0}q}\text{, }&m_{0}\neq 0\text{ and }q\neq 0\\d_{2}\in \mathrm{R}\text{, }&R=p\text{ and }\left(m_{0}=0\text{ or }q=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$p+qm_{0}d_{2}=R$$

Subtract p from both sides.

$$qm_{0}d_{2}=R-p$$

The equation is in standard form.

$$m_{0}qd_{2}=R-p$$

Divide both sides by qm_{0}.

$$\frac{m_{0}qd_{2}}{m_{0}q}=\frac{R-p}{m_{0}q}$$

Dividing by qm_{0} undoes the multiplication by qm_{0}.

$$d_{2}=\frac{R-p}{m_{0}q}$$

Solve for R

$$R=d_{2}m_{0}q+p$$