Answer
{$-5,\frac{3}{4}$}
Work Step by Step
Using the rules of factoring trinomials to factor the polynomial, we obtain:
$4t^{2}+17t-15=0$
$4t^{2}-3t+20t-15=0$
$t(4t-3)+5(4t-3)=0$
$(4t-3)(t+5)=0$
Now, we equate the two factors to zero and solve:
$(4t-3)(t+5)=0$
$(4t-3)=0$ or $(t+5)=0$
$t=\frac{3}{4}$ or $t=-5$
Therefore, the solution set is {$-5,\frac{3}{4}$}.
