Solve (x+6)^2=(x+14)(x+2)

$$( x + 6 ) ^ { 2 } = ( x + 14 ) ( x + 2 )$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$x^{2}+12x+36=\left(x+14\right)\left(x+2\right)$$

Use the distributive property to multiply x+14 by x+2 and combine like terms.

$$x^{2}+12x+36=x^{2}+16x+28$$

Subtract x^{2} from both sides.

$$x^{2}+12x+36-x^{2}=16x+28$$

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

$$12x+36=16x+28$$

Subtract 16x from both sides.

$$12x+36-16x=28$$

Combine 12x and -16x to get -4x.

$$-4x+36=28$$

Subtract 36 from both sides.

$$-4x=28-36$$

Subtract 36 from 28 to get -8.

$$-4x=-8$$

Divide both sides by -4.

$$x=\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$x=2$$