#### Answer

$\color{blue}{\left\{-27, 3\right\}}$

#### Work Step by Step

Raise both sides to the 4th power to obtain:
$((x^2+24x)^{1/4})^4=3^4
\\x^2+24x=81
\\x^2+24x-81=0$
Factor the trinomial to obtain:
$(x+27)(x-3)=0$
Use the Zero-Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
&x+27=0 &\text{or} &x-3=0
\\&x=-27 &\text{or} &x=3
\end{array}
Upon checking, both proposed solutions satisfy the original equation.
Thus, the solution set is $\color{blue}{\left\{-27, 3\right\}}$.