How do you factor 36p^2+47pq+15q^2

I can't seem to factor this, but it is factorable. Can anyone shed some light?

36p^2 + 47pq + 15q^2

First, multiply 36 and 15 to get 540. Now, we have to find the factors of 540 which add to 47, and these are 20 and 27. Using this, split the middle term like this:

36p^2 + 27pq + 20pq + 15q^2

Split into two parts:

(36p^2 + 27pq) + (20pq + 15q^2)

Factor each separately:

9p * (4p + 3q) + 5q * (4p + 3q)

Regroup to get the final factored form:

(9p + 5q) * (4p + 3q)

This works just like a quadratic. To factor it first multiply the coefficients of p^2 and q^2. This yields 540. Now find the factors of 540 that combine to make 47, the coefficient of pq. These are 20 and 27. Now rewrite your trinomial like this:

36p^2 + 20pq + 27pq + 15q^2

Now group them like this:

(36p^2 + 20pq) + (27pq + 15q^2)

Now factor each group to get:

4p(9p + 5q) + 3q(9p + 5q)

Now pull out the common factor of 9p + 5q and get:

(9p + 5q)(4p + 3q)

9p+5q 4p+3q

(9p + 5q)(4p + 3q)