Solve (x+1)^2=(x+3)(x-2)

$$( x + 1 ) ^ { 2 } = ( x + 3 ) ( x - 2 )$$

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

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

$$x^{2}+2x+1=\left(x+3\right)\left(x-2\right)$$

Use the distributive property to multiply x+3 by x-2 and combine like terms.

$$x^{2}+2x+1=x^{2}+x-6$$

Subtract x^{2} from both sides.

$$x^{2}+2x+1-x^{2}=x-6$$

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

$$2x+1=x-6$$

Subtract x from both sides.

$$2x+1-x=-6$$

Combine 2x and -x to get x.

$$x+1=-6$$

Subtract 1 from both sides.

$$x=-6-1$$

Subtract 1 from -6 to get -7.

$$x=-7$$