Answer
$x=\{ -1,0,8,9 \}$
Work Step by Step
Let $z=
x^2-8x
.$ Then the given equation, $
3\sqrt{x^2-8x}=x^2-8x
$, is equivalent to
\begin{array}{l}\require{cancel}
3\sqrt{z}=z
.\end{array}
Squaring both sides of the equal sign results to
\begin{array}{l}\require{cancel}
9\cdot z=z^2
\\\\
-z^2+9z=0
\\\\
z^2-9z=0
\\\\
z(z-9)=0
\\\\
z=\{ 0,9 \}
.\end{array}
If $z=0$, then,
\begin{array}{l}\require{cancel}
x^2-8x=0
\\\\
x(x-8)=0
\\\\
x=\{ 0,8 \}
.\end{array}
If $z=9$, then,
\begin{array}{l}\require{cancel}
x^2-8x=9
\\\\
x^2-8x-9=0
\\\\
(x-9)(x+1)=0
\\\\
x=\{ -1,9 \}
.\end{array}
The proposed solutions are $
x=\{ -1,0,8,9
.\}$ Upon checking, all the proposed solutions satisfy the original equation. Hence, $
x=\{ -1,0,8,9 \}
.$
