Given
[tex](\frac{1}{4})^{x+1}=32[/tex]Notice that
[tex]\begin{gathered} 32=2^5 \\ and \\ (\frac{1}{4})^{x+1}=\frac{1}{4^{x+1}}=4^{-(x+1)}=4^{-x-1}=2^{-2x-2} \end{gathered}[/tex]Therefore, the original equation is equivalent to
[tex]\Rightarrow2^{-2x-2}=2^5[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow-2x-2=5 \\ \Rightarrow x=-\frac{7}{2} \end{gathered}[/tex]Therefore, the answer is -7/2, option D.