Solve 0=(x8+L)xvarepsilon

$$0 = ( x 8 + L ) x \varepsilon$$

Solve for L (complex solution)

$$\left\{\begin{matrix}\\L=-x_{8}\text{, }&\text{unconditionally}\\L\in \mathrm{C}\text{, }&\epsilon =0\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x_{8}+L by x.

$$0=\left(x_{8}x+Lx\right)\epsilon$$

Use the distributive property to multiply x_{8}x+Lx by \epsilon .

$$0=x_{8}x\epsilon +Lx\epsilon$$

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

$$x_{8}x\epsilon +Lx\epsilon =0$$

Subtract x_{8}x\epsilon from both sides. Anything subtracted from zero gives its negation.

$$Lx\epsilon =-x_{8}x\epsilon$$

Reorder the terms.

$$Lx\epsilon =-xx_{8}\epsilon$$

The equation is in standard form.

$$x\epsilon L=-xx_{8}\epsilon$$

Divide both sides by x\epsilon .

$$\frac{x\epsilon L}{x\epsilon }=-\frac{xx_{8}\epsilon }{x\epsilon }$$

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

$$L=-\frac{xx_{8}\epsilon }{x\epsilon }$$

Divide -xx_{8}\epsilon by x\epsilon .

$$L=-x_{8}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&\epsilon =0\text{ or }x_{8}=-L\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x_{8}+L by x.

$$0=\left(x_{8}x+Lx\right)\epsilon$$

Use the distributive property to multiply x_{8}x+Lx by \epsilon .

$$0=x_{8}x\epsilon +Lx\epsilon$$

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

$$x_{8}x\epsilon +Lx\epsilon =0$$

Combine all terms containing x.

$$\left(x_{8}\epsilon +L\epsilon \right)x=0$$

Divide 0 by x_{8}\epsilon +L\epsilon .

$$x=0$$

Solve for L

$$\left\{\begin{matrix}\\L=-x_{8}\text{, }&\text{unconditionally}\\L\in \mathrm{R}\text{, }&\epsilon =0\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x_{8}+L by x.

$$0=\left(x_{8}x+Lx\right)\epsilon$$

Use the distributive property to multiply x_{8}x+Lx by \epsilon .

$$0=x_{8}x\epsilon +Lx\epsilon$$

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

$$x_{8}x\epsilon +Lx\epsilon =0$$

Subtract x_{8}x\epsilon from both sides. Anything subtracted from zero gives its negation.

$$Lx\epsilon =-x_{8}x\epsilon$$

Reorder the terms.

$$Lx\epsilon =-xx_{8}\epsilon$$

The equation is in standard form.

$$x\epsilon L=-xx_{8}\epsilon$$

Divide both sides by x\epsilon .

$$\frac{x\epsilon L}{x\epsilon }=-\frac{xx_{8}\epsilon }{x\epsilon }$$

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

$$L=-\frac{xx_{8}\epsilon }{x\epsilon }$$

Divide -xx_{8}\epsilon by x\epsilon .

$$L=-x_{8}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\epsilon =0\text{ or }x_{8}=-L\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x_{8}+L by x.

$$0=\left(x_{8}x+Lx\right)\epsilon$$

Use the distributive property to multiply x_{8}x+Lx by \epsilon .

$$0=x_{8}x\epsilon +Lx\epsilon$$

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

$$x_{8}x\epsilon +Lx\epsilon =0$$

Combine all terms containing x.

$$\left(x_{8}\epsilon +L\epsilon \right)x=0$$

Divide 0 by x_{8}\epsilon +L\epsilon .

$$x=0$$