$$\frac{7m}{9}+\frac{m-3}{6}=\frac{6m}{9}-\frac{2}{6}$$
$m=\frac{3}{5}=0.6$
$$2\times 7m+3\left(m-3\right)=2\times 6m-3\times 2$$
$$14m+3\left(m-3\right)=2\times 6m-3\times 2$$
$$14m+3m-9=2\times 6m-3\times 2$$
$$17m-9=2\times 6m-3\times 2$$
$$17m-9=12m-6$$
$$17m-9-12m=-6$$
$$5m-9=-6$$
$$5m=-6+9$$
$$5m=3$$
$$m=\frac{3}{5}$$
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