Solve for m
m=\frac{-4\sin(3x)+3}{2}
Solve for x
x=\frac{\arcsin(\frac{3-2m}{4})+2\pi n_{1}}{3}\text{, }n_{1}\in \mathrm{Z}
x=\frac{-\arcsin(\frac{3-2m}{4})+2\pi n_{2}+\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }m\geq -\frac{1}{2}\text{ and }m\leq \frac{7}{2}
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2m=3-4\sin(3x)
Subtract 4\sin(3x) from both sides.
2m=-4\sin(3x)+3
The equation is in standard form.
\frac{2m}{2}=\frac{-4\sin(3x)+3}{2}
Divide both sides by 2.
m=\frac{-4\sin(3x)+3}{2}
Dividing by 2 undoes the multiplication by 2.
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