Solve F(x+2)(x-2)=8(x-1)

$$F ( x + 2 ) ( x - 2 ) = 8 ( x - 1 )$$

Solve for F (complex solution)

$$F=-\frac{8\left(1-x\right)}{x^{2}-4}$$

$$x\neq -2\text{ and }x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply F by x+2.

$$\left(Fx+2F\right)\left(x-2\right)=8\left(x-1\right)$$

Use the distributive property to multiply Fx+2F by x-2 and combine like terms.

$$Fx^{2}-4F=8\left(x-1\right)$$

Use the distributive property to multiply 8 by x-1.

$$Fx^{2}-4F=8x-8$$

Combine all terms containing F.

$$\left(x^{2}-4\right)F=8x-8$$

Divide both sides by x^{2}-4.

$$\frac{\left(x^{2}-4\right)F}{x^{2}-4}=\frac{8x-8}{x^{2}-4}$$

Dividing by x^{2}-4 undoes the multiplication by x^{2}-4.

$$F=\frac{8x-8}{x^{2}-4}$$

Divide -8+8x by x^{2}-4.

$$F=\frac{8\left(x-1\right)}{x^{2}-4}$$

Solve for F

$$F=-\frac{8\left(1-x\right)}{x^{2}-4}$$

$$|x|\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply F by x+2.

$$\left(Fx+2F\right)\left(x-2\right)=8\left(x-1\right)$$

Use the distributive property to multiply Fx+2F by x-2 and combine like terms.

$$Fx^{2}-4F=8\left(x-1\right)$$

Use the distributive property to multiply 8 by x-1.

$$Fx^{2}-4F=8x-8$$

Combine all terms containing F.

$$\left(x^{2}-4\right)F=8x-8$$

Divide both sides by x^{2}-4.

$$\frac{\left(x^{2}-4\right)F}{x^{2}-4}=\frac{8x-8}{x^{2}-4}$$

Dividing by x^{2}-4 undoes the multiplication by x^{2}-4.

$$F=\frac{8x-8}{x^{2}-4}$$

Divide -8+8x by x^{2}-4.

$$F=\frac{8\left(x-1\right)}{x^{2}-4}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\left(\sqrt{F^{2}-2F+4}+2\right)}{F}\text{; }x=\frac{2\left(-\sqrt{F^{2}-2F+4}+2\right)}{F}\text{, }&F\neq 0\\x=1\text{, }&F=0\end{matrix}\right.$$