Answer
$t = 1, 9$
Work Step by Step
$3(t-5)^{2} - 18 = 30$
$3(t-5)^{2} = 30 + 18$
$3(t-5)^{2} = 48$
$(t-5)^{2} = 16$
$t(t-5)-5(t-5) = 16$
$t^{2} - 5t - 5t + 25 = 16$
$t^{2} - 10t + 25 = 16$
$t^{2} - 10t + 25 - 16 = 0$
$t^{2} - 10t + 9 = 0$
$t^{2}-9t-t+9 = 0$
$t(t-9)-1(t-9) = 0$
$(t - 1)(t-9) = 0$
$t = 1, 9$
Check:
When $t = 1$
$3(1-5)^{2} - 18 \overset{?}{=} 30$
$3(-4)^{2} - 18 \overset{?}{=} 30$
$3(16) - 18 \overset{?}{=} 30$
$48 - 18 \overset{?}{=} 30$
$30 = 30$
When $t = 9$
$3(9-5)^{2} - 18 \overset{?}{=} 30$
$3(4)^{2} - 18 \overset{?}{=} 30$
$3(16) - 18 \overset{?}{=} 30$
$48 - 18 \overset{?}{=} 30$
$30 = 30$
