Sure, here is the translated text:

```
Solve the equation:
\[
\left|\begin{array}{ccc}
-4 & 2 & -4+3 i \\
3 & -5 & 2-5 i \\
-4+3 i & 2-5 i & x
\end{array}\right|=0
\]
```
$$
\begin{array}{l}
\because\left|\begin{array}{lcc}
-4 & 2 & -4+3 \mathrm{i} \\
8 & -5 & 2-5 \mathrm{i} \\
-4+3 \mathrm{i} & 2-5 \mathrm{i} & \mathbf{x}
\end{array}\right| \begin{array}{l}
\text { (multiply the first row by } \\
\text { the row above) }
\end{array} \\
\left|\begin{array}{ccc}
-4 & 2 & -4+3 i \\
3 & -5 & 2-5 i \\
3 & -5 i & x+4-3 i
\end{array}\right| \text { (multiply the second row by }-\mathrm{i} \\
\left|\begin{array}{rrl}
-4 & 2 & -4+3 i \\
8 & -5 & 2-5 i \\
0 & 0 & x-1-5 i
\end{array}\right|=(x-1-5 i)\left|\begin{array}{rr}
-4 & 2 \\
3 & -5
\end{array}\right| \\
=14(x-1-5 i)=0 \text {, } \\
\therefore x=1+5 i \text {. } \\
\end{array}
$$