To factorize a quadratic equation, you need two numbers that multiply to c, 7, and add to b, 8.
Two numbers that mutiply to 7 and add to 8 are 7 and 1.
x^2+7x+x+7
Now group them together:
x(x+7)+1(x+7)
Since (x+7) is common, you can take that as a common factor.
(x+1)(x+7)
Hope this helps :)