#### Answer

$\{0,6,9\}$

#### Work Step by Step

$-2t^{3}=108t-30t^{2}$
$-2t^{3}-108t+30t^{2}=0$
$-2t^{3}+30t^{2}-108t=0$
Factor out the GCF, $-2t$
$-2t(t^{2}-15t+54)=0$
Factoring the equation.
$-2t(t-9)(t-6)=0$
Setting each factor to zero.
$-2t = 0$
$t= 0$
OR
$t-9=0$
$t=9$
OR
$t-6=0$
$t=6$
Solution set is $\{0,6,9\}$