Solve (x-2)*(x+2)-(x+3)^2=-1

$$( x - 2 ) \cdot ( x + 2 ) - ( x + 3 ) ^ { 2 } = - 1$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

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.

$$x^{2}-4-\left(x+3\right)^{2}=-1$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}-4-\left(x^{2}+6x+9\right)=-1$$

To find the opposite of x^{2}+6x+9, find the opposite of each term.

$$x^{2}-4-x^{2}-6x-9=-1$$

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

$$-4-6x-9=-1$$

Subtract 9 from -4 to get -13.

$$-13-6x=-1$$

Add 13 to both sides.

$$-6x=-1+13$$

Add -1 and 13 to get 12.

$$-6x=12$$

Divide both sides by -6.

$$x=\frac{12}{-6}$$

Divide 12 by -6 to get -2.

$$x=-2$$