$$\frac{2n-1}{3}+\frac{-3m+2}{2}-m+\frac{7}{2}=3m$$
$m=\frac{4n+25}{33}$
$$2\left(2n-1\right)+3\left(-3m+2\right)-6m+21=18m$$
$$4n-2+3\left(-3m+2\right)-6m+21=18m$$
$$4n-2-9m+6-6m+21=18m$$
$$4n+4-9m-6m+21=18m$$
$$4n+4-15m+21=18m$$
$$4n+25-15m=18m$$
$$4n+25-15m-18m=0$$
$$4n+25-33m=0$$
$$25-33m=-4n$$
$$-33m=-4n-25$$
$$\frac{-33m}{-33}=\frac{-4n-25}{-33}$$
$$m=\frac{-4n-25}{-33}$$
$$m=\frac{4n+25}{33}$$
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$n=\frac{33m-25}{4}$
$$4n-15m=18m-25$$
$$4n=18m-25+15m$$
$$4n=33m-25$$
$$\frac{4n}{4}=\frac{33m-25}{4}$$
$$n=\frac{33m-25}{4}$$
