#### Answer

$m=0$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
3(5+3m)-8=7
$, is
\begin{array}{l}
15+9m-8=7
\\\\
9m=7-15+8
\\\\
9m=0
\\\\
m=0
.\end{array}
CHECKING:
\begin{array}{l}
3(5+3\cdot0)-8=7
\\\\
3(5)-8=7
\\\\
15-8=7
\\\\
7=7
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
m=0
$.