#### Answer

The solutions are $m=2$ and $m=5$.

#### Work Step by Step

Let
$u=m-6$
Rewrite the given equation using the variable $u$ to obtain:
$u^2+5u+4=0$
Factor the trinomial to obtain:
$(u+4)(u+1)=0$
Use the Zero-Factor Property by equating each unique factor to zero. then solve:
$u+4 = 0 \text{ or } u+1=0
\\u=-4 \text{ or } u=-1$
Since $u=m-6$, then
\begin{array}{ccc}
&u= -4 &\text{or} &u=-1
\\&m-6=-4 &\text{or} &m-6=-1
\\&m=-4+6 &\text{or} &m=-1+6
\\&m=2 &\text{or} &m=5
\end{array}
Thus, the solutions are $m=2$ and $m=5$.