Simplify 3 square root of 10 end root plus 7 square root of 15 end root minus 6 square root of 10 end root minus 4 square root of 15

Start with

We can factor the square root of 10 between the 1st and 3rd term, and the square root of 15 between the remaining two:

Now we can factor 3 from both terms:

You can also use the rule

To observe that

So we can factor the square root of 5 as well:

And the expression is fully simplified.

$12. that is my answer.