Solve nx-x=(n+3)(n+2)

$$n x - x = ( n + 3 ) ( n + 2 )$$

Solve for x

$$x=\frac{\left(n+2\right)\left(n+3\right)}{n-1}$$

$$n\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply n+3 by n+2 and combine like terms.

$$nx-x=n^{2}+5n+6$$

Combine all terms containing x.

$$\left(n-1\right)x=n^{2}+5n+6$$

Divide both sides by n-1.

$$\frac{\left(n-1\right)x}{n-1}=\frac{\left(n+2\right)\left(n+3\right)}{n-1}$$

Dividing by n-1 undoes the multiplication by n-1.

$$x=\frac{\left(n+2\right)\left(n+3\right)}{n-1}$$

Solve for n (complex solution)

$$n=\frac{-\sqrt{x^{2}-14x+1}+x-5}{2}$$

$$n=\frac{\sqrt{x^{2}-14x+1}+x-5}{2}$$

Solve for n

$$n=\frac{-\sqrt{x^{2}-14x+1}+x-5}{2}$$

$$n=\frac{\sqrt{x^{2}-14x+1}+x-5}{2}\text{, }x\geq 4\sqrt{3}+7\text{ or }x\leq 7-4\sqrt{3}$$