#### Answer

$n=-5$

#### Work Step by Step

Using the properties of equality and combining like terms, the value of the variable that satisfies the given equation, $
-3n+6+5n=7n-8n-9
,$ is
\begin{array}{l}\require{cancel}
-3n+5n-7n+8n=-9-6
\\\\
3n=-15
\\\\
n=\dfrac{-15}{3}
\\\\
n=-5
.\end{array}