10c² + 25c – 6c – 15

Factor the first two terms 10c² + 25c by taking out the
greatest common factor, getting 5c(2c+5) 

Factor the last two terms -6c-15 by taking out the
greatest common factor, -3, getting -3(2c+5)

So we have

5c(2c+5)-3(2c+5)

Notice that there is a common factor, (2c+5)

5c(2c+5)-3(2x-3)

which we can factor out leaving the 5c and the -3 to put 
in parentheses:

(2c+5)(5c-3)

Edwin