$$3(t-3)=5(2t+1)$$
$t=-2$
$$3t-9=5\left(2t+1\right)$$
$$3t-9=10t+5$$
$$3t-9-10t=5$$
$$-7t-9=5$$
$$-7t=5+9$$
$$-7t=14$$
$$t=\frac{14}{-7}$$
$$t=-2$$
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