Solve fg(x)=3x(3-x)

$$f g ( x ) = 3 x ( 3 - x )$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{3\left(x-3\right)}{g}\text{, }&g\neq 0\\f\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=3\text{ and }g=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 3-x.

$$fgx=9x-3x^{2}$$

The equation is in standard form.

$$gxf=9x-3x^{2}$$

Divide both sides by gx.

$$\frac{gxf}{gx}=\frac{3x\left(3-x\right)}{gx}$$

Dividing by gx undoes the multiplication by gx.

$$f=\frac{3x\left(3-x\right)}{gx}$$

Divide 3x\left(3-x\right) by gx.

$$f=\frac{3\left(3-x\right)}{g}$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{3\left(x-3\right)}{f}\text{, }&f\neq 0\\g\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=3\text{ and }f=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 3-x.

$$fgx=9x-3x^{2}$$

The equation is in standard form.

$$fxg=9x-3x^{2}$$

Divide both sides by fx.

$$\frac{fxg}{fx}=\frac{3x\left(3-x\right)}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$g=\frac{3x\left(3-x\right)}{fx}$$

Divide 3x\left(3-x\right) by fx.

$$g=\frac{3\left(3-x\right)}{f}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{3\left(x-3\right)}{g}\text{, }&g\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=3\text{ and }g=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 3-x.

$$fgx=9x-3x^{2}$$

The equation is in standard form.

$$gxf=9x-3x^{2}$$

Divide both sides by gx.

$$\frac{gxf}{gx}=\frac{3x\left(3-x\right)}{gx}$$

Dividing by gx undoes the multiplication by gx.

$$f=\frac{3x\left(3-x\right)}{gx}$$

Divide 3x\left(3-x\right) by gx.

$$f=\frac{3\left(3-x\right)}{g}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{3\left(x-3\right)}{f}\text{, }&f\neq 0\\g\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=3\text{ and }f=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 3-x.

$$fgx=9x-3x^{2}$$

The equation is in standard form.

$$fxg=9x-3x^{2}$$

Divide both sides by fx.

$$\frac{fxg}{fx}=\frac{3x\left(3-x\right)}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$g=\frac{3x\left(3-x\right)}{fx}$$

Divide 3x\left(3-x\right) by fx.

$$g=\frac{3\left(3-x\right)}{f}$$