x2 − 2x − 15 = 0

Factoring gives:

(x − 5)(x + 3) = 0

Now, if either of the terms (x − 5) or (x + 3) is 0, the product is zero. So we conclude:

(x − 5) = 0, therefore

x = 5

or

(x + 3) = 0, therefore

x = − 3

Hence the roots are x = 5 and x = − 3.

Are we correct?

We check the roots in the original equation by substitution.

When x = 5:

x2 − 2x − 15

= (5)2 − 10 − 15

= 25 − 10 − 15

= 0

(Similarly, when we substitute `x = -3`, we also get `0`.)