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

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

Solve for x

$$x = -\frac{22}{5} = -4\frac{2}{5} = -4.4$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by x+4 and combine like terms.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+2x-8=x^{2}+12x+36$$

Subtract x^{2} from both sides.

$$x^{2}+2x-8-x^{2}=12x+36$$

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

$$2x-8=12x+36$$

Subtract 12x from both sides.

$$2x-8-12x=36$$

Combine 2x and -12x to get -10x.

$$-10x-8=36$$

Add 8 to both sides.

$$-10x=36+8$$

Add 36 and 8 to get 44.

$$-10x=44$$

Divide both sides by -10.

$$x=\frac{44}{-10}$$

Reduce the fraction \frac{44}{-10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{22}{5}$$