How can f (x) = 6x^2+5x-6 be factored to reveal the zeros of the function it defines

6 x^2+5 x-6

Factor the quadratic 6 x^2+5 x-6. The coefficient of x^2 is 6 and the constant term is - 6. The product of 6 and - 6 is - 36. The factors of - 36 which sum to 5 are - 4 and 9. So 6 x^2+5 x-6 = 6 x^2+9 x-4 x-6 = 3 (3 x-2) + 2 x (3 x-2):

3 (3 x-2) + 2 x (3 x-2)

Factor 3 x-2 from 3 (3 x-2) + 2 x (3 x-2):

Answer: |

| (3 x-2) (2 x+3)

Zeros: 2/3, - 3/2