Solve fx=12left(x-2right)^2

$$fx=12 { \left(x-2 \right) }^{ 2 }$$

Solve for f

$$f=\frac{12\left(x-2\right)^{2}}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 12 by x^{2}-4x+4.

$$fx=12x^{2}-48x+48$$

The equation is in standard form.

$$xf=12x^{2}-48x+48$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{12\left(x-2\right)^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{12\left(x-2\right)^{2}}{x}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{f\left(f+96\right)}+f+48}{24}$$

$$x=\frac{\sqrt{f\left(f+96\right)}+f+48}{24}$$

Solve for x

$$x=\frac{-\sqrt{f\left(f+96\right)}+f+48}{24}$$

$$x=\frac{\sqrt{f\left(f+96\right)}+f+48}{24}\text{, }f\leq -96\text{ or }f\geq 0$$