the difference between two times the square of a number and five times the number is 75. Look at the red words: the difference between two times the square of a number and five times the number is 75. Replace each by x. the difference between two times the square of x and five times x is 75. Look at the blue words: the difference between two times the square of x and five times x is 75. Replace them by x² the difference between two times x² and five times x is 75. Look at the red words: the difference between two times x² and five times x is 75. Replace them by 5x the difference between two times x² and 5x is 75 Look at the blue words: the difference between two times x² and 5x is 75. Replace them by 2x² the difference between 2x² and 5x is 75. Look at the red words: the difference between 2x² and 5x is 75. Replace them by the subtraction of the first minus the second, or 2x² - 5x 2x² - 5x is 75. Look at the blue word: 2x² - 5x is 75. Replace it by an equal sign " = ": 2x² - 5x = 75. Solve that: 2x² - 5x - 75 = 0 Factoring: (2x - 15)(x + 5) = 0 2x - 15 = 0 gives solution x =x + 5 = 0 gives solution x = -5 Edwin