Solve nf(x)=-2(x-1)(x+3)

$$n f ( x ) = - 2 ( x - 1 ) ( x + 3 )$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{2\left(x-1\right)\left(x+3\right)}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\f\in \mathrm{C}\text{, }&\left(x=1\text{ or }x=-3\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$nfx=\left(-2x+2\right)\left(x+3\right)$$

Use the distributive property to multiply -2x+2 by x+3 and combine like terms.

$$nfx=-2x^{2}-4x+6$$

The equation is in standard form.

$$nxf=6-4x-2x^{2}$$

Divide both sides by nx.

$$\frac{nxf}{nx}=\frac{2\left(1-x\right)\left(x+3\right)}{nx}$$

Dividing by nx undoes the multiplication by nx.

$$f=\frac{2\left(1-x\right)\left(x+3\right)}{nx}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{2\left(x-1\right)\left(x+3\right)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\n\in \mathrm{C}\text{, }&\left(x=1\text{ or }x=-3\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$nfx=\left(-2x+2\right)\left(x+3\right)$$

Use the distributive property to multiply -2x+2 by x+3 and combine like terms.

$$nfx=-2x^{2}-4x+6$$

The equation is in standard form.

$$fxn=6-4x-2x^{2}$$

Divide both sides by fx.

$$\frac{fxn}{fx}=\frac{2\left(1-x\right)\left(x+3\right)}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$n=\frac{2\left(1-x\right)\left(x+3\right)}{fx}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{2\left(x-1\right)\left(x+3\right)}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\f\in \mathrm{R}\text{, }&\left(x=1\text{ or }x=-3\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$nfx=\left(-2x+2\right)\left(x+3\right)$$

Use the distributive property to multiply -2x+2 by x+3 and combine like terms.

$$nfx=-2x^{2}-4x+6$$

The equation is in standard form.

$$nxf=6-4x-2x^{2}$$

Divide both sides by nx.

$$\frac{nxf}{nx}=\frac{2\left(1-x\right)\left(x+3\right)}{nx}$$

Dividing by nx undoes the multiplication by nx.

$$f=\frac{2\left(1-x\right)\left(x+3\right)}{nx}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{2\left(x-1\right)\left(x+3\right)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\n\in \mathrm{R}\text{, }&\left(x=1\text{ or }x=-3\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-1.

$$nfx=\left(-2x+2\right)\left(x+3\right)$$

Use the distributive property to multiply -2x+2 by x+3 and combine like terms.

$$nfx=-2x^{2}-4x+6$$

The equation is in standard form.

$$fxn=6-4x-2x^{2}$$

Divide both sides by fx.

$$\frac{fxn}{fx}=\frac{2\left(1-x\right)\left(x+3\right)}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$n=\frac{2\left(1-x\right)\left(x+3\right)}{fx}$$