$$3(t-1)-2(2t+3)=5(t+3)$$
$t=-4$
$$3t-3-2\left(2t+3\right)=5\left(t+3\right)$$
$$3t-3-4t-6=5\left(t+3\right)$$
$$-t-3-6=5\left(t+3\right)$$
$$-t-9=5\left(t+3\right)$$
$$-t-9=5t+15$$
$$-t-9-5t=15$$
$$-6t-9=15$$
$$-6t=15+9$$
$$-6t=24$$
$$t=\frac{24}{-6}$$
$$t=-4$$
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