First, rewrite the radicals as:
#-6sqrt(16 * 5) + 2sqrt(25 * 3) - 8sqrt(49 * 5) - 14sqrt(36 * 3)#
Next, use this rule for radicals to simplify the radicals:
#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#
#-6sqrt(color(red)(16) * color(blue)(5)) + 2sqrt(color(red)(25) * color(blue)(3)) - 8sqrt(color(red)(49) * color(blue)(5)) - 14sqrt(color(red)(36) * color(blue)(3)) =>#
#-6sqrt(color(red)(16))sqrt(color(blue)(5)) + 2sqrt(color(red)(25))sqrt(color(blue)(3)) - 8sqrt(color(red)(49))sqrt(color(blue)(5)) - 14sqrt(color(red)(36))sqrt(color(blue)(3)) =>#
#(-6 * 4sqrt(color(blue)(5))) + (2 * 5sqrt(color(blue)(3))) - (8 * 7sqrt(color(blue)(5))) - (14 * 6sqrt(color(blue)(3))) =>#
#-24sqrt(color(blue)(5)) + 10sqrt(color(blue)(3)) - 56sqrt(color(blue)(5)) - 84sqrt(color(blue)(3))#
Then group and combine like terms:
#-24sqrt(color(blue)(5)) - 56sqrt(color(blue)(5)) + 10sqrt(color(blue)(3)) - 84sqrt(color(blue)(3)) =>#
#(-24 - 56)sqrt(5) + (10 - 84)sqrt(3) =>#
#-80sqrt(5) + (-74)sqrt(3) =>#
#-80sqrt(5) - 74sqrt(3)#
