Solve (x+y)(x-y)=3n

$$( x + y ) ( x - y ) = 3 n$$

Solve for n

$$n=\frac{x^{2}-y^{2}}{3}$$

Steps for Solving Linear Equation

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-y^{2}=3n$$

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

$$3n=x^{2}-y^{2}$$

Divide both sides by 3.

$$\frac{3n}{3}=\frac{\left(x-y\right)\left(x+y\right)}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$n=\frac{\left(x-y\right)\left(x+y\right)}{3}$$

Solve for x (complex solution)

$$x=-\sqrt{y^{2}+3n}$$

$$x=\sqrt{y^{2}+3n}$$

Solve for x

$$x=\sqrt{y^{2}+3n}$$

$$x=-\sqrt{y^{2}+3n}\text{, }n\geq -\frac{y^{2}}{3}$$