Question

factor this trinomial completely.

Answer 1

start by moving 3b out, so you have
3b(2b^2 - 5b-12), then solve the quadratic equation

Answer 2

where do you get 3b?

Answer 3

@jayda 3b is the greatest monomial factor of 6b^3 + 15 b^2 - 36b. That is, 3b is a factor of 6b^3, 15b^2 and -36b.
So, 6b^3 + 15 b^2 - 36b = 3b(2b^2 + 5b - 12).
The task now is to determine if (2b^2 + 5b - 12) factors.
It does factor into (b + 4) (2b -3)
The final factorization of the trinomial is the following:

6b^3 + 15 b^2 - 36b = 3b (b + 4) (2b -3).
Please check my work. Thanks.