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

$$(x-2)(x+1)= { x }^{ 2 } -1x-2$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

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

Subtract x^{2} from both sides.

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

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

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

Add x to both sides.

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

Combine -x and x to get 0.

$$-2=-2$$

Compare -2 and -2.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

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

Subtract x^{2} from both sides.

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

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

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

Add x to both sides.

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

Combine -x and x to get 0.

$$-2=-2$$

Compare -2 and -2.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$