Solve (x+7)(x+1)=left(x+1right)^2

$$(x+7)(x+1)= { \left(x+1 \right) }^{ 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+7 by x+1 and combine like terms.

$$x^{2}+8x+7=\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}+8x+7=x^{2}+2x+1$$

Subtract x^{2} from both sides.

$$x^{2}+8x+7-x^{2}=2x+1$$

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

$$8x+7=2x+1$$

Subtract 2x from both sides.

$$8x+7-2x=1$$

Combine 8x and -2x to get 6x.

$$6x+7=1$$

Subtract 7 from both sides.

$$6x=1-7$$

Subtract 7 from 1 to get -6.

$$6x=-6$$

Divide both sides by 6.

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

Divide -6 by 6 to get -1.

$$x=-1$$