(7w-6)(9w-5);   7x9=63; so try factors of 30:  both are of the same sign (-), since the last term is + and the middle term is (-).  10x3 doesn't work, so 6 and 5 work; 6x9=54 and 5x7=35, adding to 89.

ax² + bx + c = a(x - x₁)(x - x₂) , x₁ and x₂ are roots of equation
ax² + bx + c = 0 and x_1,2 = (-b ± √D)/2a , D = b² - 4ac 
~~~~~~~~~~~
55n² - 52n + 12 = 0 , D = 52² - 4 · 55 · 12 = 64
n₁ = (52 + 8)/110 = 6/11
n₂ = (52 – 8)/110 = 2/5
55(n – 6/11)(n – 2/5) = (11n – 6)(5n – 2)

(11n + 3)(5n + 4)

The key here is recognizing that 55 is the product of two (and two only) primes - 5 and 11. The rest of the problem works itself out