Solve fg(x)=9x^2+6x-4

$$f g ( x ) = 9 x ^ { 2 } + 6 x - 4$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{4-6x-9x^{2}}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\f\in \mathrm{C}\text{, }&\left(x=\frac{-\sqrt{5}-1}{3}\text{ or }x=\frac{\sqrt{5}-1}{3}\right)\text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$gxf=9x^{2}+6x-4$$

Divide both sides by gx.

$$\frac{gxf}{gx}=\frac{9x^{2}+6x-4}{gx}$$

Dividing by gx undoes the multiplication by gx.

$$f=\frac{9x^{2}+6x-4}{gx}$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{4-6x-9x^{2}}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\g\in \mathrm{C}\text{, }&\left(x=\frac{-\sqrt{5}-1}{3}\text{ or }x=\frac{\sqrt{5}-1}{3}\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$fxg=9x^{2}+6x-4$$

Divide both sides by fx.

$$\frac{fxg}{fx}=\frac{9x^{2}+6x-4}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$g=\frac{9x^{2}+6x-4}{fx}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{4-6x-9x^{2}}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\f\in \mathrm{R}\text{, }&\left(x=\frac{-\sqrt{5}-1}{3}\text{ or }x=\frac{\sqrt{5}-1}{3}\right)\text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$gxf=9x^{2}+6x-4$$

Divide both sides by gx.

$$\frac{gxf}{gx}=\frac{9x^{2}+6x-4}{gx}$$

Dividing by gx undoes the multiplication by gx.

$$f=\frac{9x^{2}+6x-4}{gx}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{4-6x-9x^{2}}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\g\in \mathrm{R}\text{, }&\left(x=\frac{-\sqrt{5}-1}{3}\text{ or }x=\frac{\sqrt{5}-1}{3}\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$fxg=9x^{2}+6x-4$$

Divide both sides by fx.

$$\frac{fxg}{fx}=\frac{9x^{2}+6x-4}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$g=\frac{9x^{2}+6x-4}{fx}$$