#### Answer

$r=\dfrac{-6t-2}{a-3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
ar+2=3r-6t
,$ for $
r
,$ put all variables with $
r
$ on the left side of the equation and all other terms on the right side. Then use the properties of equality to isolate $
r
.$
$\bf{\text{Solution Details:}}$
Putting all terms with $r$ on the left side of the equation and all other terms on the right side, the equation above is equivalent to
\begin{array}{l}\require{cancel}
ar-3r=-6t-2
.\end{array}
Factoring $r$ on the left side and then isolating it result to
\begin{array}{l}\require{cancel}
r(a-3)=-6t-2
\\\\
r=\dfrac{-6t-2}{a-3}
.\end{array}