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3xy=-6+4\cos(x)
Add 4\cos(x) to both sides.
3xy=4\cos(x)-6
The equation is in standard form.
\frac{3xy}{3x}=\frac{2\left(2\cos(x)-3\right)}{3x}
Divide both sides by 3x.
y=\frac{2\left(2\cos(x)-3\right)}{3x}
Dividing by 3x undoes the multiplication by 3x.