Solve y=-2f(x+1)-2

$$y = - 2 f ( x + 1 ) - 2$$

Solve for f (complex solution)

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

Steps for Solving Linear Equation

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

$$y=-2fx-2f-2$$

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

$$-2fx-2f-2=y$$

Add 2 to both sides.

$$-2fx-2f=y+2$$

Combine all terms containing f.

$$\left(-2x-2\right)f=y+2$$

Divide both sides by -2x-2.

$$\frac{\left(-2x-2\right)f}{-2x-2}=\frac{y+2}{-2x-2}$$

Dividing by -2x-2 undoes the multiplication by -2x-2.

$$f=\frac{y+2}{-2x-2}$$

Divide y+2 by -2x-2.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{-y-2f-2}{2f}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=-2\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=-2fx-2f-2$$

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

$$-2fx-2f-2=y$$

Add 2f to both sides.

$$-2fx-2=y+2f$$

Add 2 to both sides.

$$-2fx=y+2f+2$$

The equation is in standard form.

$$\left(-2f\right)x=y+2f+2$$

Divide both sides by -2f.

$$\frac{\left(-2f\right)x}{-2f}=\frac{y+2f+2}{-2f}$$

Dividing by -2f undoes the multiplication by -2f.

$$x=\frac{y+2f+2}{-2f}$$

Divide y+2+2f by -2f.

$$x=-\frac{y+2f+2}{2f}$$

Solve for f

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

Steps for Solving Linear Equation

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

$$y=-2fx-2f-2$$

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

$$-2fx-2f-2=y$$

Add 2 to both sides.

$$-2fx-2f=y+2$$

Combine all terms containing f.

$$\left(-2x-2\right)f=y+2$$

Divide both sides by -2x-2.

$$\frac{\left(-2x-2\right)f}{-2x-2}=\frac{y+2}{-2x-2}$$

Dividing by -2x-2 undoes the multiplication by -2x-2.

$$f=\frac{y+2}{-2x-2}$$

Divide y+2 by -2x-2.

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

Solve for x

$$\left\{\begin{matrix}x=\frac{-y-2f-2}{2f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=-2\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=-2fx-2f-2$$

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

$$-2fx-2f-2=y$$

Add 2f to both sides.

$$-2fx-2=y+2f$$

Add 2 to both sides.

$$-2fx=y+2f+2$$

The equation is in standard form.

$$\left(-2f\right)x=y+2f+2$$

Divide both sides by -2f.

$$\frac{\left(-2f\right)x}{-2f}=\frac{y+2f+2}{-2f}$$

Dividing by -2f undoes the multiplication by -2f.

$$x=\frac{y+2f+2}{-2f}$$

Divide y+2+2f by -2f.

$$x=-\frac{y+2f+2}{2f}$$