#### Answer

$n=\{ -20,20 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|3n|=60
,$ use the definition of absolute value equality. Then use the properties of equality to solve the variable.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
3n=60
\\\\\text{OR}\\\\
3n=-60
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3n=60
\\\\
n=\dfrac{60}{3}
\\\\
n=20
\\\\\text{OR}\\\\
3n=-60
\\\\
n=-\dfrac{60}{3}
\\\\
n=-20
.\end{array}
Hence, $
n=\{ -20,20 \}
.$