Solve (x-2)(x+3)-[(x+5)(x-7)]=2

$$( x - 2 ) ( x + 3 ) - [ ( x + 5 ) ( x - 7 ) ] = 2$$

Solve for x

$$x=-9$$

Steps for Solving Linear Equation

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

$$x^{2}+x-6-\left(x+5\right)\left(x-7\right)=2$$

Use the distributive property to multiply x+5 by x-7 and combine like terms.

$$x^{2}+x-6-\left(x^{2}-2x-35\right)=2$$

To find the opposite of x^{2}-2x-35, find the opposite of each term.

$$x^{2}+x-6-x^{2}+2x+35=2$$

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

$$x-6+2x+35=2$$

Combine x and 2x to get 3x.

$$3x-6+35=2$$

Add -6 and 35 to get 29.

$$3x+29=2$$

Subtract 29 from both sides.

$$3x=2-29$$

Subtract 29 from 2 to get -27.

$$3x=-27$$

Divide both sides by 3.

$$x=\frac{-27}{3}$$

Divide -27 by 3 to get -9.

$$x=-9$$