Solve (y+3)(y+3)-(y+2)(y-2)=2y+1

$$( y + 3 ) ( y + 3 ) - ( y + 2 ) ( y - 2 ) = 2 y + 1$$

Solve for y

$$y=-3$$

Steps for Solving Linear Equation

Multiply y+3 and y+3 to get \left(y+3\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+3\right)^{2}.

$$y^{2}+6y+9-\left(y+2\right)\left(y-2\right)=2y+1$$

Consider \left(y+2\right)\left(y-2\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 2.

$$y^{2}+6y+9-\left(y^{2}-4\right)=2y+1$$

To find the opposite of y^{2}-4, find the opposite of each term.

$$y^{2}+6y+9-y^{2}+4=2y+1$$

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

$$6y+9+4=2y+1$$

Add 9 and 4 to get 13.

$$6y+13=2y+1$$

Subtract 2y from both sides.

$$6y+13-2y=1$$

Combine 6y and -2y to get 4y.

$$4y+13=1$$

Subtract 13 from both sides.

$$4y=1-13$$

Subtract 13 from 1 to get -12.

$$4y=-12$$

Divide both sides by 4.

$$y=\frac{-12}{4}$$

Divide -12 by 4 to get -3.

$$y=-3$$