Hi!
(x+a)·(x+b) = x²+xa+xb+ab = x²-12x-45
x² = x²
xa+xb = (a+b)x = -12x ⇒ (a+b) = -12
ab = -45
When (a+b) = -12 and ab = -45?
+3-15 = -12 and (+3)(-15) = -45
-3-15 = -18 and (-3)(-15) = +45
+3+15 = +18 and (+3)(+15) = +45
-3+15 = +12 and (-3+15) = -45
Answer:
(x+3)(x-15)