Answer
{$-3,4$}
Work Step by Step
Given: $3|2x-1|=21$
This can also be written as: $|2x-1|=7$
As per definition of absolute value, we have
$2x-1=7$ and $2x-1=-7$
Thus, $2x=8 \implies x=4$ and $2x=-6 \implies x=-3$
Hence, {$-3,4$}