Answer
$t = -9, 3$
Work Step by Step
$-2(t+3)^{2} - 8 = -80$
$-2(t+3)^{2} = -80 + 8$
$-2(t+3)^{2} = -72$
$(t+3)^{2} = 36$
$t + 3 = ±\sqrt {36}$
$t = ±6 - 3$
$t = -9, 3$
Check:
When $t = -9$
$-2(-9+3)^{2} - 8 \overset{?}{=} -80$
$-2(-6)^{2} - 8 \overset{?}{=} -80$
$-2(36) - 8 \overset{?}{=} -80$
$-72 - 8 \overset{?}{=} -80$
$-80\overset{?}{=} -80$
When $t = 3$
$-2(3+3)^{2} - 8 \overset{?}{=} -80$
$-2(6)^{2} - 8 \overset{?}{=} -80$
$-2(36) - 8 \overset{?}{=} -80$
$-72 - 8 \overset{?}{=} -80$
$-80\overset{?}{=} -80$
