$$\frac { n } { 2 } - \frac { 3 n } { 4 } + \frac { 5 m } { 6 } = 21$$
$m=\frac{3\left(n+84\right)}{10}$
$$6n-3\times 3n+2\times 5m=252$$
$$6n-9n+2\times 5m=252$$
$$-3n+2\times 5m=252$$
$$-3n+10m=252$$
$$10m=252+3n$$
$$10m=3n+252$$
$$\frac{10m}{10}=\frac{3n+252}{10}$$
$$m=\frac{3n+252}{10}$$
$$m=\frac{3n}{10}+\frac{126}{5}$$
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$n=\frac{10m}{3}-84$
$$-3n=252-10m$$
$$\frac{-3n}{-3}=\frac{252-10m}{-3}$$
$$n=\frac{252-10m}{-3}$$
$$n=\frac{10m}{3}-84$$
