Answer
$t=-1.5$, $t= 6.5$
Work Step by Step
Given \begin{equation}
-3|2 t-5|=-24.
\end{equation}
The absolute value equation can be solved as shown below:
\begin{equation}
\begin{aligned}
\frac{-3|2 t-5|}{-3}&=\frac{-24}{-3} \\
|2 t-5|&= 8.
\end{aligned}
\end{equation} This gives \begin{equation}
\begin{aligned}
2 t-5&=-8 \quad \text { or } \quad 2 t-5=8\\
t&= \frac{-8+5}{2}\quad \text { or } \quad t= \frac{8+5}{2}\\
t&= -\frac{3}{2}\quad \text { or } t= \frac{13}{2}.
\end{aligned}
\end{equation} Check
\begin{equation}
\begin{aligned}
-3|2 \cdot (-1.5)-5|& \stackrel{?}{=}-24 \\
-24& =-24\ \textbf{True}\\
-3|2 \cdot (6.5)-5|& \stackrel{?}{=}-24 \\
-24& =-24\ \textbf{True}
\end{aligned}
\end{equation} The solution is $$t=-1.5,\quad t= 6.5.$$
