Solve x^2+(n+1)x+n=0

$$x ^ { 2 } + ( n + 1 ) x + n = 0$$

Solve for n (complex solution)

$$\left\{\begin{matrix}\\n=-x\text{, }&\text{unconditionally}\\n\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n+1 by x.

$$x^{2}+nx+x+n=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$nx+x+n=-x^{2}$$

Subtract x from both sides.

$$nx+n=-x^{2}-x$$

Combine all terms containing n.

$$\left(x+1\right)n=-x^{2}-x$$

Divide both sides by 1+x.

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

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

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

Divide -x\left(1+x\right) by 1+x.

$$n=-x$$

Solve for n

$$\left\{\begin{matrix}\\n=-x\text{, }&\text{unconditionally}\\n\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n+1 by x.

$$x^{2}+nx+x+n=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$nx+x+n=-x^{2}$$

Subtract x from both sides.

$$nx+n=-x^{2}-x$$

Combine all terms containing n.

$$\left(x+1\right)n=-x^{2}-x$$

Divide both sides by 1+x.

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

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

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

Divide -x\left(1+x\right) by 1+x.

$$n=-x$$

Solve for x

$$x=-n$$

$$x=-1$$