Solve n(x-6)^2=4

$$n ( x - 6 ) ^ { 2 } = 4$$

Solve for n

$$n=\frac{4}{\left(x-6\right)^{2}}$$

$$x\neq 6$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$n\left(x^{2}-12x+36\right)=4$$

Use the distributive property to multiply n by x^{2}-12x+36.

$$nx^{2}-12nx+36n=4$$

Combine all terms containing n.

$$\left(x^{2}-12x+36\right)n=4$$

Divide both sides by x^{2}-12x+36.

$$\frac{\left(x^{2}-12x+36\right)n}{x^{2}-12x+36}=\frac{4}{x^{2}-12x+36}$$

Dividing by x^{2}-12x+36 undoes the multiplication by x^{2}-12x+36.

$$n=\frac{4}{x^{2}-12x+36}$$

Divide 4 by x^{2}-12x+36.

$$n=\frac{4}{\left(x-6\right)^{2}}$$

Solve for x (complex solution)

$$x=2n^{-\frac{1}{2}}+6$$

$$x=6-2n^{-\frac{1}{2}}\text{, }n\neq 0$$

Solve for x

$$x=6+\frac{2}{\sqrt{n}}$$

$$x=6-\frac{2}{\sqrt{n}}\text{, }n>0$$