Factor the polynomial completely 12x^4-42x^3-90x^2

Factor the following:
12 x^4 - 42 x^3 - 90 x^2

Factor 6 x^2 out of 12 x^4 - 42 x^3 - 90 x^2:
6 x^2 (2 x^2 - 7 x - 15)

Factor the quadratic 2 x^2 - 7 x - 15. The coefficient of x^2 is 2 and the constant term is -15. The product of 2 and -15 is -30. The factors of -30 which sum to -7 are 3 and -10. So 2 x^2 - 7 x - 15 = 2 x^2 - 10 x + 3 x - 15 = x (2 x + 3) - 5 (2 x + 3):
6 x^2 x (2 x + 3) - 5 (2 x + 3)

Factor 2 x + 3 from x (2 x + 3) - 5 (2 x + 3):
  6 x^2 (2 x + 3) (x - 5)