Solve 0=(2/varepsilon-x)z

$$0 = ( \frac { 2 } { \varepsilon } - x ) z$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2}{\epsilon }\text{, }&\epsilon \neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }\epsilon \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$0=\left(\frac{2}{\epsilon }-x\right)z\epsilon$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\epsilon }{\epsilon }.

$$0=\left(\frac{2}{\epsilon }-\frac{x\epsilon }{\epsilon }\right)z\epsilon$$

Since \frac{2}{\epsilon } and \frac{x\epsilon }{\epsilon } have the same denominator, subtract them by subtracting their numerators.

$$0=\frac{2-x\epsilon }{\epsilon }z\epsilon$$

Express \frac{2-x\epsilon }{\epsilon }z as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon$$

Express \frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z\epsilon }{\epsilon }$$

Cancel out \epsilon in both numerator and denominator.

$$0=z\left(-x\epsilon +2\right)$$

Use the distributive property to multiply z by -x\epsilon +2.

$$0=-zx\epsilon +2z$$

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

$$-zx\epsilon +2z=0$$

Subtract 2z from both sides. Anything subtracted from zero gives its negation.

$$-zx\epsilon =-2z$$

The equation is in standard form.

$$\left(-z\epsilon \right)x=-2z$$

Divide both sides by -z\epsilon .

$$\frac{\left(-z\epsilon \right)x}{-z\epsilon }=-\frac{2z}{-z\epsilon }$$

Dividing by -z\epsilon undoes the multiplication by -z\epsilon .

$$x=-\frac{2z}{-z\epsilon }$$

Divide -2z by -z\epsilon .

$$x=\frac{2}{\epsilon }$$

Solve for z (complex solution)

$$\left\{\begin{matrix}z=0\text{, }&\epsilon \neq 0\\z\in \mathrm{C}\text{, }&\epsilon =\frac{2}{x}\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$0=\left(\frac{2}{\epsilon }-x\right)z\epsilon$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\epsilon }{\epsilon }.

$$0=\left(\frac{2}{\epsilon }-\frac{x\epsilon }{\epsilon }\right)z\epsilon$$

Since \frac{2}{\epsilon } and \frac{x\epsilon }{\epsilon } have the same denominator, subtract them by subtracting their numerators.

$$0=\frac{2-x\epsilon }{\epsilon }z\epsilon$$

Express \frac{2-x\epsilon }{\epsilon }z as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon$$

Express \frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z\epsilon }{\epsilon }$$

Cancel out \epsilon in both numerator and denominator.

$$0=z\left(-x\epsilon +2\right)$$

Use the distributive property to multiply z by -x\epsilon +2.

$$0=-zx\epsilon +2z$$

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

$$-zx\epsilon +2z=0$$

Combine all terms containing z.

$$\left(-x\epsilon +2\right)z=0$$

The equation is in standard form.

$$\left(2-x\epsilon \right)z=0$$

Divide 0 by 2-\epsilon x.

$$z=0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2}{\epsilon }\text{, }&\epsilon \neq 0\\x\in \mathrm{R}\text{, }&z=0\text{ and }\epsilon \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$0=\left(\frac{2}{\epsilon }-x\right)z\epsilon$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\epsilon }{\epsilon }.

$$0=\left(\frac{2}{\epsilon }-\frac{x\epsilon }{\epsilon }\right)z\epsilon$$

Since \frac{2}{\epsilon } and \frac{x\epsilon }{\epsilon } have the same denominator, subtract them by subtracting their numerators.

$$0=\frac{2-x\epsilon }{\epsilon }z\epsilon$$

Express \frac{2-x\epsilon }{\epsilon }z as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon$$

Express \frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z\epsilon }{\epsilon }$$

Cancel out \epsilon in both numerator and denominator.

$$0=z\left(-x\epsilon +2\right)$$

Use the distributive property to multiply z by -x\epsilon +2.

$$0=-zx\epsilon +2z$$

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

$$-zx\epsilon +2z=0$$

Subtract 2z from both sides. Anything subtracted from zero gives its negation.

$$-zx\epsilon =-2z$$

The equation is in standard form.

$$\left(-z\epsilon \right)x=-2z$$

Divide both sides by -z\epsilon .

$$\frac{\left(-z\epsilon \right)x}{-z\epsilon }=-\frac{2z}{-z\epsilon }$$

Dividing by -z\epsilon undoes the multiplication by -z\epsilon .

$$x=-\frac{2z}{-z\epsilon }$$

Divide -2z by -z\epsilon .

$$x=\frac{2}{\epsilon }$$

Solve for z

$$\left\{\begin{matrix}z=0\text{, }&\epsilon \neq 0\\z\in \mathrm{R}\text{, }&\epsilon =\frac{2}{x}\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \epsilon .

$$0=\left(\frac{2}{\epsilon }-x\right)z\epsilon$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\epsilon }{\epsilon }.

$$0=\left(\frac{2}{\epsilon }-\frac{x\epsilon }{\epsilon }\right)z\epsilon$$

Since \frac{2}{\epsilon } and \frac{x\epsilon }{\epsilon } have the same denominator, subtract them by subtracting their numerators.

$$0=\frac{2-x\epsilon }{\epsilon }z\epsilon$$

Express \frac{2-x\epsilon }{\epsilon }z as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon$$

Express \frac{\left(2-x\epsilon \right)z}{\epsilon }\epsilon as a single fraction.

$$0=\frac{\left(2-x\epsilon \right)z\epsilon }{\epsilon }$$

Cancel out \epsilon in both numerator and denominator.

$$0=z\left(-x\epsilon +2\right)$$

Use the distributive property to multiply z by -x\epsilon +2.

$$0=-zx\epsilon +2z$$

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

$$-zx\epsilon +2z=0$$

Combine all terms containing z.

$$\left(-x\epsilon +2\right)z=0$$

The equation is in standard form.

$$\left(2-x\epsilon \right)z=0$$

Divide 0 by 2-\epsilon x.

$$z=0$$