$$15(y-4)-2(x-9)+5(y+6)=0$$
$x=10y-6$
$$15y-60-2\left(x-9\right)+5\left(y+6\right)=0$$
$$15y-60-2x+18+5\left(y+6\right)=0$$
$$15y-42-2x+5\left(y+6\right)=0$$
$$15y-42-2x+5y+30=0$$
$$20y-42-2x+30=0$$
$$20y-12-2x=0$$
$$-12-2x=-20y$$
$$-2x=-20y+12$$
$$-2x=12-20y$$
$$\frac{-2x}{-2}=\frac{12-20y}{-2}$$
$$x=\frac{12-20y}{-2}$$
$$x=10y-6$$
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$y=\frac{x+6}{10}$
$$20y-2x=12$$
$$20y=12+2x$$
$$20y=2x+12$$
$$\frac{20y}{20}=\frac{2x+12}{20}$$
$$y=\frac{2x+12}{20}$$
$$y=\frac{x}{10}+\frac{3}{5}$$
