Solve (x+1)(x-3)=x^2+mx+n

$$( x + 1 ) ( x - 3 ) = x ^ { 2 } + m x + n$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{2x+n+3}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$x^{2}-2x-3=x^{2}+mx+n$$

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

$$x^{2}+mx+n=x^{2}-2x-3$$

Subtract x^{2} from both sides.

$$mx+n=x^{2}-2x-3-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$mx+n=-2x-3$$

Subtract n from both sides.

$$mx=-2x-3-n$$

The equation is in standard form.

$$xm=-2x-n-3$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{-2x-n-3}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{-2x-n-3}{x}$$

Divide -2x-3-n by x.

$$m=-\frac{2x+n+3}{x}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{2x+n+3}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }n=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$x^{2}-2x-3=x^{2}+mx+n$$

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

$$x^{2}+mx+n=x^{2}-2x-3$$

Subtract x^{2} from both sides.

$$mx+n=x^{2}-2x-3-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$mx+n=-2x-3$$

Subtract n from both sides.

$$mx=-2x-3-n$$

The equation is in standard form.

$$xm=-2x-n-3$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{-2x-n-3}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{-2x-n-3}{x}$$

Divide -2x-3-n by x.

$$m=-\frac{2x+n+3}{x}$$

Solve for n

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

Solution Steps

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$x^{2}-2x-3=x^{2}+mx+n$$

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

$$x^{2}+mx+n=x^{2}-2x-3$$

Subtract x^{2} from both sides.

$$mx+n=x^{2}-2x-3-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$mx+n=-2x-3$$

Subtract mx from both sides.

$$n=-2x-3-mx$$