Solve (x+1)^2-(x+1)(x-2)=6

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

Solve for x

$$x=1$$

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}.

$$x^{2}+2x+1-\left(x+1\right)\left(x-2\right)=6$$

Use the distributive property to multiply x+1 by x-2 and combine like terms.

$$x^{2}+2x+1-\left(x^{2}-x-2\right)=6$$

To find the opposite of x^{2}-x-2, find the opposite of each term.

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

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

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

Combine 2x and x to get 3x.

$$3x+1+2=6$$

Add 1 and 2 to get 3.

$$3x+3=6$$

Subtract 3 from both sides.

$$3x=6-3$$

Subtract 3 from 6 to get 3.

$$3x=3$$

Divide both sides by 3.

$$x=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$x=1$$