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

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

Solve for y

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

$$n\neq 6\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply n\left(-y\right) by n-6.

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

Multiply -6 and -1 to get 6.

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

Reorder the terms.

$$-yn^{2}+6ny=168$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -n^{2}+6n.

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

Dividing by -n^{2}+6n undoes the multiplication by -n^{2}+6n.

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

Divide 168 by -n^{2}+6n.

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

Solve for n (complex solution)

$$n=\frac{\sqrt{9y^{2}-168y}}{y}+3$$

$$n=-\frac{\sqrt{9y^{2}-168y}}{y}+3\text{, }y\neq 0$$

Solve for n

$$n=\frac{\sqrt{9y^{2}-168y}}{y}+3$$

$$n=-\frac{\sqrt{9y^{2}-168y}}{y}+3\text{, }y<0\text{ or }y\geq \frac{56}{3}$$