Solve (x+2)(x+1)=(x+4)(x+5)

$$( x + 2 ) ( x + 1 ) = ( x + 4 ) ( x + 5 )$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x+4 by x+5 and combine like terms.

$$x^{2}+3x+2=x^{2}+9x+20$$

Subtract x^{2} from both sides.

$$x^{2}+3x+2-x^{2}=9x+20$$

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

$$3x+2=9x+20$$

Subtract 9x from both sides.

$$3x+2-9x=20$$

Combine 3x and -9x to get -6x.

$$-6x+2=20$$

Subtract 2 from both sides.

$$-6x=20-2$$

Subtract 2 from 20 to get 18.

$$-6x=18$$

Divide both sides by -6.

$$x=\frac{18}{-6}$$

Divide 18 by -6 to get -3.

$$x=-3$$