Solve x^2 - 2x - 15 = 0

This is a simple quadratic equation. To answer the question, it must first be factorised before it can be solved. To do this, two numbers need to be found which multiply to make the constant term and have a difference equal to the coefficient of the x term. In this instance, the two numbers are 5 and 3.

Write down (x 5) (x 3) = 0

The two signs missing above can be found by looking first at the sign in front of the constant, the minus sign indicated the signs missing above will be different (one positive, one negative). Next, by looking at the sign in front of the coefficient of x (another minus) you can deduce the bigger value of the two above (the 5) will have the minus sign and the smaller (the 3) will have the plus sign in front.

Write (x - 5) (x + 3) = 0

It can be said, if the multiple of 2 numbers is equal to zero, then one of those numbers must be 0. Therefore you can say that (x - 5) = 0 or (x + 3) = 0. Simple algebra will therefore show that x = 5 or x = -3.