Solve h(x)=xoperatorname{an}x

$$h ( x ) = x \operatorname { an } x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{h}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\a\in \mathrm{C}\text{, }&\left(h=0\text{ and }n=0\text{ and }x\neq 0\right)\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$hx=x^{2}an$$

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

$$x^{2}an=hx$$

The equation is in standard form.

$$nx^{2}a=hx$$

Divide both sides by x^{2}n.

$$\frac{nx^{2}a}{nx^{2}}=\frac{hx}{nx^{2}}$$

Dividing by x^{2}n undoes the multiplication by x^{2}n.

$$a=\frac{hx}{nx^{2}}$$

Divide hx by x^{2}n.

$$a=\frac{h}{nx}$$

Solve for h (complex solution)

$$\left\{\begin{matrix}\\h=anx\text{, }&\text{unconditionally}\\h\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$hx=x^{2}an$$

The equation is in standard form.

$$xh=anx^{2}$$

Divide both sides by x.

$$\frac{xh}{x}=\frac{anx^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$h=\frac{anx^{2}}{x}$$

Divide x^{2}an by x.

$$h=anx$$

Solve for a

$$\left\{\begin{matrix}a=\frac{h}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\a\in \mathrm{R}\text{, }&\left(h=0\text{ and }n=0\text{ and }x\neq 0\right)\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$hx=x^{2}an$$

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

$$x^{2}an=hx$$

The equation is in standard form.

$$nx^{2}a=hx$$

Divide both sides by x^{2}n.

$$\frac{nx^{2}a}{nx^{2}}=\frac{hx}{nx^{2}}$$

Dividing by x^{2}n undoes the multiplication by x^{2}n.

$$a=\frac{hx}{nx^{2}}$$

Divide hx by x^{2}n.

$$a=\frac{h}{nx}$$

Solve for h

$$\left\{\begin{matrix}\\h=anx\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$hx=x^{2}an$$

The equation is in standard form.

$$xh=anx^{2}$$

Divide both sides by x.

$$\frac{xh}{x}=\frac{anx^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$h=\frac{anx^{2}}{x}$$

Divide x^{2}an by x.

$$h=anx$$