Solve y=(x+1)(x-a)

$$y = ( x + 1 ) ( x - a )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x^{2}+x-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=x^{2}-xa+x-a$$

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

$$x^{2}-xa+x-a=y$$

Subtract x^{2} from both sides.

$$-xa+x-a=y-x^{2}$$

Subtract x from both sides.

$$-xa-a=y-x^{2}-x$$

Combine all terms containing a.

$$\left(-x-1\right)a=y-x^{2}-x$$

The equation is in standard form.

$$\left(-x-1\right)a=y-x-x^{2}$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)a}{-x-1}=\frac{y-x-x^{2}}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$a=\frac{y-x-x^{2}}{-x-1}$$

Divide -x^{2}-x+y by -x-1.

$$a=-\frac{y-x-x^{2}}{x+1}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x^{2}+x-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=x^{2}-xa+x-a$$

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

$$x^{2}-xa+x-a=y$$

Subtract x^{2} from both sides.

$$-xa+x-a=y-x^{2}$$

Subtract x from both sides.

$$-xa-a=y-x^{2}-x$$

Combine all terms containing a.

$$\left(-x-1\right)a=y-x^{2}-x$$

The equation is in standard form.

$$\left(-x-1\right)a=y-x-x^{2}$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)a}{-x-1}=\frac{y-x-x^{2}}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$a=\frac{y-x-x^{2}}{-x-1}$$

Divide y-x^{2}-x by -x-1.

$$a=-\frac{y-x-x^{2}}{x+1}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{4y+a^{2}+2a+1}+a-1}{2}$$

$$x=\frac{\sqrt{4y+a^{2}+2a+1}+a-1}{2}$$

Solve for x

$$x=\frac{-\sqrt{4y+a^{2}+2a+1}+a-1}{2}$$

$$x=\frac{\sqrt{4y+a^{2}+2a+1}+a-1}{2}\text{, }y\geq -\frac{\left(a+1\right)^{2}}{4}$$