Solve (x-1)(x+2)=2+(x+3)(x-4)

$$( x - 1 ) ( x + 2 ) = 2 + ( x + 3 ) ( x - 4 )$$

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x+3 by x-4 and combine like terms.

$$x^{2}+x-2=2+x^{2}-x-12$$

Subtract 12 from 2 to get -10.

$$x^{2}+x-2=-10+x^{2}-x$$

Subtract x^{2} from both sides.

$$x^{2}+x-2-x^{2}=-10-x$$

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

$$x-2=-10-x$$

Add x to both sides.

$$x-2+x=-10$$

Combine x and x to get 2x.

$$2x-2=-10$$

Add 2 to both sides.

$$2x=-10+2$$

Add -10 and 2 to get -8.

$$2x=-8$$

Divide both sides by 2.

$$x=\frac{-8}{2}$$

Divide -8 by 2 to get -4.

$$x=-4$$