Solve x=axbeta

$$x = a x \beta$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$ax\beta =x$$

The equation is in standard form.

$$x\beta a=x$$

Divide both sides by x\beta .

$$\frac{x\beta a}{x\beta }=\frac{x}{x\beta }$$

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

$$a=\frac{x}{x\beta }$$

Divide x by x\beta .

$$a=\frac{1}{\beta }$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract ax\beta from both sides.

$$x-ax\beta =0$$

Reorder the terms.

$$-ax\beta +x=0$$

Combine all terms containing x.

$$\left(-a\beta +1\right)x=0$$

The equation is in standard form.

$$\left(1-a\beta \right)x=0$$

Divide 0 by 1-a\beta .

$$x=0$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ax\beta =x$$

The equation is in standard form.

$$x\beta a=x$$

Divide both sides by x\beta .

$$\frac{x\beta a}{x\beta }=\frac{x}{x\beta }$$

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

$$a=\frac{x}{x\beta }$$

Divide x by x\beta .

$$a=\frac{1}{\beta }$$

Solve for x

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

Steps for Solving Linear Equation

Subtract ax\beta from both sides.

$$x-ax\beta =0$$

Reorder the terms.

$$-ax\beta +x=0$$

Combine all terms containing x.

$$\left(-a\beta +1\right)x=0$$

The equation is in standard form.

$$\left(1-a\beta \right)x=0$$

Divide 0 by 1-a\beta .

$$x=0$$