Answer
{$-\frac{7}{2},\frac{1}{3}$}
Work Step by Step
First, we factor the expression by using the trinomial rules of factoring. Then, we equate the resultant factors to zero.
$6t^{2}+19t-7=0$
$6t^{2}+21t-2t-7=0$
$3t(2t+7)-1(2t+7)=0$
$(2t+7)(3t-1)=0$
$(2t+7)=0$ and $(3t-1)=0$
$2t=-7$ and $3t=1$
$t=-\frac{7}{2}$ and $t=\frac{1}{3}$
Therefore, the solution set is {$-\frac{7}{2},\frac{1}{3}$}.
