Solve x+varepsilonvarphix=0

$$x + \varepsilon \varphi x = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&\epsilon =-\frac{1}{\phi }\text{ and }\phi \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(1+\epsilon \phi \right)x=0$$

The equation is in standard form.

$$\left(\epsilon \phi +1\right)x=0$$

Divide 0 by 1+\epsilon \phi .

$$x=0$$

Solve for ε (complex solution)

$$\left\{\begin{matrix}\epsilon =-\frac{1}{\phi }\text{, }&\phi \neq 0\\\epsilon \in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\epsilon \phi x=-x$$

The equation is in standard form.

$$x\phi \epsilon =-x$$

Divide both sides by \phi x.

$$\frac{x\phi \epsilon }{x\phi }=-\frac{x}{x\phi }$$

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

$$\epsilon =-\frac{x}{x\phi }$$

Divide -x by \phi x.

$$\epsilon =-\frac{1}{\phi }$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\epsilon =-\frac{1}{\phi }\text{ and }\phi \neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(1+\epsilon \phi \right)x=0$$

The equation is in standard form.

$$\left(\epsilon \phi +1\right)x=0$$

Divide 0 by 1+\epsilon \phi .

$$x=0$$

Solve for ε

$$\left\{\begin{matrix}\epsilon =-\frac{1}{\phi }\text{, }&\phi \neq 0\\\epsilon \in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\epsilon \phi x=-x$$

The equation is in standard form.

$$x\phi \epsilon =-x$$

Divide both sides by \phi x.

$$\frac{x\phi \epsilon }{x\phi }=-\frac{x}{x\phi }$$

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

$$\epsilon =-\frac{x}{x\phi }$$

Divide -x by \phi x.

$$\epsilon =-\frac{1}{\phi }$$