Solve (x+5)^2=(x+5)(x-5)

$$( x + 5 ) ^ { 2 } = ( x + 5 ) ( x - 5 )$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$x^{2}+10x+25=\left(x+5\right)\left(x-5\right)$$

Consider \left(x+5\right)\left(x-5\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 5.

$$x^{2}+10x+25=x^{2}-25$$

Subtract x^{2} from both sides.

$$x^{2}+10x+25-x^{2}=-25$$

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

$$10x+25=-25$$

Subtract 25 from both sides.

$$10x=-25-25$$

Subtract 25 from -25 to get -50.

$$10x=-50$$

Divide both sides by 10.

$$x=\frac{-50}{10}$$

Divide -50 by 10 to get -5.

$$x=-5$$