Question 310585
Let us first work backwards with the answer you got:

(4x+1)(12xy+5z)
=4x(12xy+5z)+1.(12xy+5z)
=48x^2y + 20xz + 12xy + 5z

However the question is 48x^2y+12xy+20xz+5x which means the factors you have calculated are incorrect because your question has +5x in the end.

Now having said that lets see how we can factorize:
48x^2y+12xy+20xz+5x
= x(48xy+12y+20z+5)
= x (12y(4x+1) + 5(4z+1))

This cannot be factorised further.