x² - 15 = 2x Get 0 on the right by adding -2x to both sides. x² - 15 - 2x = 0 Arrange the left side in descending order of eponents of x: We need to factor the left side: Give the x² the coefficient of 1 1x² - 2x - 15 = 0 Multiply the red 1 by the blue 15, getting 15. Now think of a pair of positive integers whose product is the blue 15 and whose difference is the green 2. I said difference because the last sign (before the 15) is minus. Had it been plus, I would have said "sum". We think of the integers 3 and 5 because their product is the blue 15 and their difference is the green 2. Now we use the 3 and 5 to rewrite the green -2 as 3 - 5. So we rewrite 2x as -3x + 5x. That is, x² - 2x - 15 = 0 becomes x² + 3x - 5x - 15 = 0 Now we factor x out of the first two terms x(x + 3) - 5x - 15 = 0 and factor -5 out of the last two terms on the left: x(x + 3) - 5(x + 3) = 0 Be careful to notice that when we factor a NEGATIVE number, -5, out of another NEGATIVE number -15, we get a POSITIVE 3. Now we have a common factor, which we can factor out, namely the (x + 3)'s which I color red: x(x + 3) - 5(x + 3) = 0 Factor out the red parentheses: (x + 3)(x - 5) = 0 Setting the first factor (x + 3) = 0 gives x = -3 Setting the second factor (x - 5) = 0 gives x = 5 So the solutions are -3 and 5. Edwin