Answer
$x= 32 $
Work Step by Step
Given \begin{equation}
\sqrt[3]{-4 x+3}=-5.
\end{equation} Start by rewriting the radical as a power of fraction and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[3]{-4 x+3}&=-5\\
\left(-4 x+3\right)^{\frac{1}{3}}&= -5\\
\left(\left(-4 x+3\right)^{\frac{1}{3}}\right)^3& = \left( -5\right)^3 \\
-4 x+3& =-125\\
x&= \frac{-125-3}{-4}\\
& = 32.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\left(-4\cdot(32)+3\right)^{\frac{1}{3}}&\stackrel{?}{=}-5\\
-5& =-5\quad \checkmark\\
\end{aligned}
\end{equation} The solution is $x= 32$.
