Solve 12(n*x)=30+(n-3)(n-5)

$$12 ( n \cdot x ) = 30 + ( n - 3 ) ( n - 5 )$$

Solve for x

$$x=\frac{n}{12}-\frac{2}{3}+\frac{15}{4n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-3 by n-5 and combine like terms.

$$12nx=30+n^{2}-8n+15$$

Add 30 and 15 to get 45.

$$12nx=45+n^{2}-8n$$

The equation is in standard form.

$$12nx=n^{2}-8n+45$$

Divide both sides by 12n.

$$\frac{12nx}{12n}=\frac{n^{2}-8n+45}{12n}$$

Dividing by 12n undoes the multiplication by 12n.

$$x=\frac{n^{2}-8n+45}{12n}$$

Divide 45+n^{2}-8n by 12n.

$$x=\frac{n}{12}-\frac{2}{3}+\frac{15}{4n}$$

Solve for n (complex solution)

$$n=-\sqrt{36x^{2}+48x-29}+6x+4$$

$$n=\sqrt{36x^{2}+48x-29}+6x+4$$

Solve for n

$$n=-\sqrt{36x^{2}+48x-29}+6x+4$$

$$n=\sqrt{36x^{2}+48x-29}+6x+4\text{, }x\geq \frac{\sqrt{5}}{2}-\frac{2}{3}\text{ or }x\leq -\frac{\sqrt{5}}{2}-\frac{2}{3}$$