#### Answer

$(3t+1)(7t-4)$

#### Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $-84$ and whose sum is $-5$. A little searching determines that these numbers are $7$ and $-12$. Therefore, we can express the middle term $-5t$ as $(7t-12t)$ and proceed to factoring by grouping:
$21t^{2}-5t-4$
=$21t^{2}+7t-12t-4$
=$7t(3t+1)-4(3t+1)$
=$(3t+1)(7t-4)$