Answer
$x=-1$
Work Step by Step
Subtract $4\pi$ to both sides:
$-4\cot^{-1}{(x)}=-3\pi$
Divide $-4$ to both sides:
$\cot^{-1}{(x)}=\frac{-3\pi}{-4}
\\\cot^{-1}{(x)}=\frac{3\pi}{4}$
RECALL:
$\cot^{-1}{(x)} = \theta \longrightarrow \cot{\theta} = x$
Use the rule above to obtain:
$\cot^{-1}{(x)} = \frac{3\pi}{4}
\\\cot{(\frac{3\pi}{4})}=x
\\-1=x$
