Solve (x+2)(x-2)-(x+4)^2=6

$$( x + 2 ) ( x - 2 ) - ( x + 4 ) ^ { 2 } = 6$$

Solve for x

$$x = -\frac{13}{4} = -3\frac{1}{4} = -3.25$$

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.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}-4-\left(x^{2}+8x+16\right)=6$$

To find the opposite of x^{2}+8x+16, find the opposite of each term.

$$x^{2}-4-x^{2}-8x-16=6$$

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

$$-4-8x-16=6$$

Subtract 16 from -4 to get -20.

$$-20-8x=6$$

Add 20 to both sides.

$$-8x=6+20$$

Add 6 and 20 to get 26.

$$-8x=26$$

Divide both sides by -8.

$$x=\frac{26}{-8}$$

Reduce the fraction \frac{26}{-8} to lowest terms by extracting and canceling out 2.

$$x=-\frac{13}{4}$$