Solve (x+1)(x+1)=left(x+2right)left(x-2right)

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

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$\left(x+1\right)^{2}=\left(x+2\right)\left(x-2\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}+2x+1=\left(x+2\right)\left(x-2\right)$$

Consider \left(x+2\right)\left(x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$x^{2}+2x+1=x^{2}-4$$

Subtract x^{2} from both sides.

$$x^{2}+2x+1-x^{2}=-4$$

Combine x^{2} and -x^{2} to get 0.

$$2x+1=-4$$

Subtract 1 from both sides.

$$2x=-4-1$$

Subtract 1 from -4 to get -5.

$$2x=-5$$

Divide both sides by 2.

$$x=\frac{-5}{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$x=-\frac{5}{2}$$