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

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

Solve for x

$$x=-\frac{1}{8}=-0.125$$

Steps for Solving Linear Equation

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

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

Add 2 and 1 to get 3.

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

Use the distributive property to multiply x+2 by x+3 and combine like terms.

$$x^{2}-3x+3=x^{2}+5x+6-2$$

Subtract 2 from 6 to get 4.

$$x^{2}-3x+3=x^{2}+5x+4$$

Subtract x^{2} from both sides.

$$x^{2}-3x+3-x^{2}=5x+4$$

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

$$-3x+3=5x+4$$

Subtract 5x from both sides.

$$-3x+3-5x=4$$

Combine -3x and -5x to get -8x.

$$-8x+3=4$$

Subtract 3 from both sides.

$$-8x=4-3$$

Subtract 3 from 4 to get 1.

$$-8x=1$$

Divide both sides by -8.

$$x=\frac{1}{-8}$$

Fraction \frac{1}{-8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$x=-\frac{1}{8}$$