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

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

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply x-3 by x+1 and combine like terms.

$$x^{2}-2x-3=x^{2}-2x-3$$

Subtract x^{2} from both sides.

$$x^{2}-2x-3-x^{2}=-2x-3$$

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

$$-2x-3=-2x-3$$

Add 2x to both sides.

$$-2x-3+2x=-3$$

Combine -2x and 2x to get 0.

$$-3=-3$$

Compare -3 and -3.

$$\text{true}$$

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-3 by x+1 and combine like terms.

$$x^{2}-2x-3=x^{2}-2x-3$$

Subtract x^{2} from both sides.

$$x^{2}-2x-3-x^{2}=-2x-3$$

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

$$-2x-3=-2x-3$$

Add 2x to both sides.

$$-2x-3+2x=-3$$

Combine -2x and 2x to get 0.

$$-3=-3$$

Compare -3 and -3.

$$\text{true}$$

This is true for any x.

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