Solve xleft(a+2right)+left(a-2right)left(a-2right)=0

$$x \left( a+2 \right) + \left( a-2 \right) \left( a-2 \right) =0$$

Solve for x

$$x=-\frac{\left(a-2\right)^{2}}{a+2}$$

$$a\neq -2$$

Steps for Solving Linear Equation

Multiply a-2 and a-2 to get \left(a-2\right)^{2}.

$$x\left(a+2\right)+\left(a-2\right)^{2}=0$$

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

$$xa+2x+\left(a-2\right)^{2}=0$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-2\right)^{2}.

$$xa+2x+a^{2}-4a+4=0$$

Subtract a^{2} from both sides. Anything subtracted from zero gives its negation.

$$xa+2x-4a+4=-a^{2}$$

Add 4a to both sides.

$$xa+2x+4=-a^{2}+4a$$

Subtract 4 from both sides.

$$xa+2x=-a^{2}+4a-4$$

Combine all terms containing x.

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

Divide both sides by a+2.

$$\frac{\left(a+2\right)x}{a+2}=-\frac{\left(a-2\right)^{2}}{a+2}$$

Dividing by a+2 undoes the multiplication by a+2.

$$x=-\frac{\left(a-2\right)^{2}}{a+2}$$

Solve for a (complex solution)

$$a=\frac{\sqrt{x\left(x-16\right)}-x+4}{2}$$

$$a=\frac{-\sqrt{x\left(x-16\right)}-x+4}{2}$$

Solve for a

$$a=\frac{\sqrt{x\left(x-16\right)}-x+4}{2}$$

$$a=\frac{-\sqrt{x\left(x-16\right)}-x+4}{2}\text{, }x\geq 16\text{ or }x\leq 0$$