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We are looking for a factorization like
6x² + 7x - 5 = (_x + _)(_x - _)
where we need to fill in the numbers in the blanks. Since the first and third blanks multiply to 6, they have to be 1 and 6 or 2 and 3. Similarly, the second and fourth blanks multiply to 5 so they must be 1 and 5. By trial and error, we arrive at the factorization
6x² + 7x - 5 = (2x - 1)(3x + 5).
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