Given (y + 1)(2y – 3) = 25, then y = what? (Don’t guess!)
So we play it straight:
(y + 1)(2y – 3) = 25
2y2 – 3y + 2y – 3 = 25
2y2 – y -28 = 0
(y – 4)(2y + 7) = 0
y = 4 or y = -7/2.
2y2 – 3y + 2y – 3 = 25
2y2 – y -28 = 0
(y – 4)(2y + 7) = 0
y = 4 or y = -7/2.
If we had thought, “hmm, 25 is 5 x 5, so let’s suppose y + 1 = 5 and 2y – 3 = 5. We would have found y = 4 but we would have missed y = -7/2:
(-7/2 + 1)(2 · -7/2 – 3) = -5/2 · -10 = 25 also.