Solve 0=2bpi+xvarepsilon*(v

$$0 = 2 b \pi + x \varepsilon \cdot ( v$$

Solve for v (complex solution)

$$\left\{\begin{matrix}v=-\frac{2\pi b}{x\epsilon }\text{, }&\epsilon \neq 0\text{ and }x\neq 0\\v\in \mathrm{C}\text{, }&\left(\epsilon =0\text{ or }x=0\right)\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2b\pi +x\epsilon v=0$$

Subtract 2b\pi from both sides. Anything subtracted from zero gives its negation.

$$x\epsilon v=-2b\pi$$

The equation is in standard form.

$$x\epsilon v=-2\pi b$$

Divide both sides by x\epsilon .

$$\frac{x\epsilon v}{x\epsilon }=-\frac{2\pi b}{x\epsilon }$$

Dividing by x\epsilon undoes the multiplication by x\epsilon .

$$v=-\frac{2\pi b}{x\epsilon }$$

Solve for b

$$b=-\frac{vx\epsilon }{2\pi }$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2b\pi +x\epsilon v=0$$

Subtract x\epsilon v from both sides. Anything subtracted from zero gives its negation.

$$2b\pi =-x\epsilon v$$

Reorder the terms.

$$2\pi b=-vx\epsilon$$

Divide both sides by 2\pi .

$$\frac{2\pi b}{2\pi }=-\frac{vx\epsilon }{2\pi }$$

Dividing by 2\pi undoes the multiplication by 2\pi .

$$b=-\frac{vx\epsilon }{2\pi }$$

Solve for v

$$\left\{\begin{matrix}v=-\frac{2\pi b}{x\epsilon }\text{, }&\epsilon \neq 0\text{ and }x\neq 0\\v\in \mathrm{R}\text{, }&\left(\epsilon =0\text{ or }x=0\right)\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2b\pi +x\epsilon v=0$$

Subtract 2b\pi from both sides. Anything subtracted from zero gives its negation.

$$x\epsilon v=-2b\pi$$

The equation is in standard form.

$$x\epsilon v=-2\pi b$$

Divide both sides by x\epsilon .

$$\frac{x\epsilon v}{x\epsilon }=-\frac{2\pi b}{x\epsilon }$$

Dividing by x\epsilon undoes the multiplication by x\epsilon .

$$v=-\frac{2\pi b}{x\epsilon }$$