49p²-84pq+36q² factor

You're in luck.

When faced with a monster like this, take some time to look it over.

Notice that the first term is a square, the last term is a square, and

the middle term is double the product of the square roots. Noticing

this, you realize immediately that the whole thing is a perfect square,

and you can write its equivalent by inspection:

49p² - 84pq + 36q² = (7p - 6q) ²