Solve Cn=(n-1)(n-2)

$$C n = ( n - 1 ) ( n - 2 )$$

Solve for C

$$C=n-3+\frac{2}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by n-2 and combine like terms.

$$Cn=n^{2}-3n+2$$

The equation is in standard form.

$$nC=n^{2}-3n+2$$

Divide both sides by n.

$$\frac{nC}{n}=\frac{\left(n-2\right)\left(n-1\right)}{n}$$

Dividing by n undoes the multiplication by n.

$$C=\frac{\left(n-2\right)\left(n-1\right)}{n}$$

Divide \left(-2+n\right)\left(-1+n\right) by n.

$$C=n-3+\frac{2}{n}$$

Solve for n (complex solution)

$$n=\frac{-\sqrt{C^{2}+6C+1}+C+3}{2}$$

$$n=\frac{\sqrt{C^{2}+6C+1}+C+3}{2}$$

Solve for n

$$n=\frac{-\sqrt{C^{2}+6C+1}+C+3}{2}$$

$$n=\frac{\sqrt{C^{2}+6C+1}+C+3}{2}\text{, }C\geq 2\sqrt{2}-3\text{ or }C\leq -2\sqrt{2}-3$$