Using simpler exponents, you know y^2 - y - 12 = (y + 3)(y - 4). That means you can factor as such:

y^(10n) - y^(5n) - 12 = (y^(5n) + 3)(y^(5n) - 4).

y^(10n) - y^(5n) - 12

= (y^(5n))^2 - y^(5n) - 12

= (y^(5n) - 4)(y^(5n) + 3)