Solve (x-5)(x+4)=(x+7)(x-6)

$$( x - 5 ) ( x + 4 ) = ( x + 7 ) ( x - 6 )$$

Solve for x

$$x=11$$

Steps for Solving Linear Equation

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

$$x^{2}-x-20=\left(x+7\right)\left(x-6\right)$$

Use the distributive property to multiply x+7 by x-6 and combine like terms.

$$x^{2}-x-20=x^{2}+x-42$$

Subtract x^{2} from both sides.

$$x^{2}-x-20-x^{2}=x-42$$

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

$$-x-20=x-42$$

Subtract x from both sides.

$$-x-20-x=-42$$

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

$$-2x-20=-42$$

Add 20 to both sides.

$$-2x=-42+20$$

Add -42 and 20 to get -22.

$$-2x=-22$$

Divide both sides by -2.

$$x=\frac{-22}{-2}$$

Divide -22 by -2 to get 11.

$$x=11$$