Solve f(x)-g(x)=0

$$f ( x ) - g ( x ) = 0$$

Solve for f (complex solution)

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

Steps for Solving Linear Equation

Add gx to both sides. Anything plus zero gives itself.

$$fx=gx$$

The equation is in standard form.

$$xf=gx$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{gx}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{gx}{x}$$

Divide gx by x.

$$f=g$$

Solve for g (complex solution)

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

Steps for Solving Linear Equation

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

$$-gx=-fx$$

Cancel out -1 on both sides.

$$gx=fx$$

The equation is in standard form.

$$xg=fx$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{fx}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{fx}{x}$$

Divide fx by x.

$$g=f$$

Solve for f

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

Steps for Solving Linear Equation

Add gx to both sides. Anything plus zero gives itself.

$$fx=gx$$

The equation is in standard form.

$$xf=gx$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{gx}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{gx}{x}$$

Divide gx by x.

$$f=g$$

Solve for g

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

Steps for Solving Linear Equation

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

$$-gx=-fx$$

Cancel out -1 on both sides.

$$gx=fx$$

The equation is in standard form.

$$xg=fx$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{fx}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{fx}{x}$$

Divide fx by x.

$$g=f$$