Solve (x+4)(x-3)=x^2+mx-n

$$( x + 4 ) ( x - 3 ) = x ^ { 2 } + m x - n$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{x+n-12}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=12\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+4 by x-3 and combine like terms.

$$x^{2}+x-12=x^{2}+mx-n$$

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

$$x^{2}+mx-n=x^{2}+x-12$$

Subtract x^{2} from both sides.

$$mx-n=x^{2}+x-12-x^{2}$$

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

$$mx-n=x-12$$

Add n to both sides.

$$mx=x-12+n$$

The equation is in standard form.

$$xm=x+n-12$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{x+n-12}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{x+n-12}{x}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{x+n-12}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }n=12\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+4 by x-3 and combine like terms.

$$x^{2}+x-12=x^{2}+mx-n$$

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

$$x^{2}+mx-n=x^{2}+x-12$$

Subtract x^{2} from both sides.

$$mx-n=x^{2}+x-12-x^{2}$$

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

$$mx-n=x-12$$

Add n to both sides.

$$mx=x-12+n$$

The equation is in standard form.

$$xm=x+n-12$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{x+n-12}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{x+n-12}{x}$$

Solve for n

$$n=mx-x+12$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+4 by x-3 and combine like terms.

$$x^{2}+x-12=x^{2}+mx-n$$

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

$$x^{2}+mx-n=x^{2}+x-12$$

Subtract x^{2} from both sides.

$$mx-n=x^{2}+x-12-x^{2}$$

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

$$mx-n=x-12$$

Subtract mx from both sides.

$$-n=x-12-mx$$

The equation is in standard form.

$$-n=-mx+x-12$$

Divide both sides by -1.

$$\frac{-n}{-1}=\frac{-mx+x-12}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$n=\frac{-mx+x-12}{-1}$$

Divide x-12-mx by -1.

$$n=mx-x+12$$