Solve (x+2)^2-(x+1)^2+5=2(x-3)+(x+3)-2

$$( x + 2 ) ^ { 2 } - ( x + 1 ) ^ { 2 } + 5 = 2 ( x - 3 ) + ( x + 3 ) - 2$$

Solve for x

$$x=13$$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4-\left(x+1\right)^{2}+5=2\left(x-3\right)+x+3-2$$

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

$$x^{2}+4x+4-\left(x^{2}+2x+1\right)+5=2\left(x-3\right)+x+3-2$$

To find the opposite of x^{2}+2x+1, find the opposite of each term.

$$x^{2}+4x+4-x^{2}-2x-1+5=2\left(x-3\right)+x+3-2$$

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

$$4x+4-2x-1+5=2\left(x-3\right)+x+3-2$$

Combine 4x and -2x to get 2x.

$$2x+4-1+5=2\left(x-3\right)+x+3-2$$

Subtract 1 from 4 to get 3.

$$2x+3+5=2\left(x-3\right)+x+3-2$$

Add 3 and 5 to get 8.

$$2x+8=2\left(x-3\right)+x+3-2$$

Use the distributive property to multiply 2 by x-3.

$$2x+8=2x-6+x+3-2$$

Combine 2x and x to get 3x.

$$2x+8=3x-6+3-2$$

Add -6 and 3 to get -3.

$$2x+8=3x-3-2$$

Subtract 2 from -3 to get -5.

$$2x+8=3x-5$$

Subtract 3x from both sides.

$$2x+8-3x=-5$$

Combine 2x and -3x to get -x.

$$-x+8=-5$$

Subtract 8 from both sides.

$$-x=-5-8$$

Subtract 8 from -5 to get -13.

$$-x=-13$$

Multiply both sides by -1.

$$x=13$$