Solve (n+y)(n-6)=168

$$( n + y ) ( n - 6 ) = 168$$

Solve for y

$$y=-\frac{n^{2}-6n-168}{n-6}$$

$$n\neq 6$$

Steps for Solving Linear Equation

Use the distributive property to multiply n+y by n-6.

$$n^{2}-6n+yn-6y=168$$

Subtract n^{2} from both sides.

$$-6n+yn-6y=168-n^{2}$$

Add 6n to both sides.

$$yn-6y=168-n^{2}+6n$$

Combine all terms containing y.

$$\left(n-6\right)y=168-n^{2}+6n$$

The equation is in standard form.

$$\left(n-6\right)y=168+6n-n^{2}$$

Divide both sides by n-6.

$$\frac{\left(n-6\right)y}{n-6}=\frac{168+6n-n^{2}}{n-6}$$

Dividing by n-6 undoes the multiplication by n-6.

$$y=\frac{168+6n-n^{2}}{n-6}$$

Solve for n

$$n=\frac{\sqrt{y^{2}+12y+708}}{2}-\frac{y}{2}+3$$

$$n=-\frac{\sqrt{y^{2}+12y+708}}{2}-\frac{y}{2}+3$$