Examine the given equation and write down the values of a, b and c. In the equation 2x² + 15x + 7, a = 2, b = 15 and c = 7. Find the product of ac: 2 x 7 = 14 and write down the possible factors: 1 and 14, 2 and 7.
Compare the sums of these factors with the value of b. In this example, the sum of factors 1 and 14 are equal to the value of b, 15. Write out the expanded equation substituting these factors for b: 2x² + x + 14x + 7. The order of the substituted factors does not affect the outcome; this equation also could be solved in the form: 2x² + 14x + x + 7.
Group the equation into two, (2x² + x) + (14x + 7), and factor out the common element in each of these groups: x(2x + 1) + 7(2x + 1). Since the terms in the parentheses are the same, they can also be factored out yielding a solution of: (x + 7)(2x + 1).