y² - 42y + 432 = 0

Now 432 is a pretty big number to express as a product of two factors. So to make your life easier, perform prime factorisation first.

432 ÷ 2 = 216
216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So 432 = 3³ × 2⁴ or 3 × 3 × 3 × 2 × 2 × 2 × 2

but we can rewrite it as :

(3 × 3 × 2) × (2 × 2 × 2 × 3)
= 18 × 24


And -18 - 24 = -42, just like how 18 + 24 = 42

So the above expression can be factorised as :


(y - 18)(y - 24) = 0

y - 18 = 0 or y - 24 = 0

y = 18 or y = 24