Solve 2sin(2x)-v3=0

$$2 \sin ( 2 x ) - v 3 = 0$$

Solve for v_3

$$v_{3}=2\sin(2x)$$

Steps for Solving Linear Equation

Subtract 2\sin(2x) from both sides. Anything subtracted from zero gives its negation.

$$-v_{3}=-2\sin(2x)$$

Divide both sides by -1.

$$\frac{-v_{3}}{-1}=-\frac{2\sin(2x)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$v_{3}=-\frac{2\sin(2x)}{-1}$$

Divide -2\sin(2x) by -1.

$$v_{3}=2\sin(2x)$$

Solve for x (complex solution)

$$x=-\frac{i\ln(\frac{i\left(\sqrt{v_{3}^{2}-4}+v_{3}\right)}{2})}{2}+\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\frac{i\ln(\frac{-i\sqrt{v_{3}^{2}-4}+iv_{3}}{2})}{2}+\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

Solve for x

$$x=\frac{\arcsin(\frac{v_{3}}{2})+2\pi n_{1}}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{-\arcsin(\frac{v_{3}}{2})+2\pi n_{2}+\pi }{2}\text{, }n_{2}\in \mathrm{Z}\text{, }|v_{3}|\leq 2$$