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

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

Solve for x

$$x=-5$$

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}.

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

Use the distributive property to multiply x by x+1.

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

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

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

Combine 4x and x to get 5x.

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

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

$$2x^{2}+5x+4=x^{2}+6x+9+x^{2}$$

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

$$2x^{2}+5x+4=2x^{2}+6x+9$$

Subtract 2x^{2} from both sides.

$$2x^{2}+5x+4-2x^{2}=6x+9$$

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

$$5x+4=6x+9$$

Subtract 6x from both sides.

$$5x+4-6x=9$$

Combine 5x and -6x to get -x.

$$-x+4=9$$

Subtract 4 from both sides.

$$-x=9-4$$

Subtract 4 from 9 to get 5.

$$-x=5$$

Multiply both sides by -1.

$$x=-5$$