Answer
The solution set is $\left\{0, 9\right\}$.
Work Step by Step
Square both sides to obtain:
$x^2=(3\sqrt{x})^2$
Use the rule $(ab)^m = a^mb^m$ to obtain:
$x^2=3^2(\sqrt{x})^2
\\x^2=9x$
Subtract $9x$ on both sides of the equation to obtain:
$x^2-9x=9x-9x
\\x^2-9x=0$
Factor out $x$ to obtain:
$x(x-9) = 0$
Equate each factor to zero, and then solve each equation to obtain:
$\begin{array}{ccc}
&x=0 &\text{ or } &x-9=0
\\&x=0 &\text{ or } &x=9
\end{array}$
Thus, the solution set is $\left\{0, 9\right\}$.
