Question 75432
Rearrange (re-group)the terms so that terms with common factors are together]
48x^2y+20xz+12xy+5z
(48x^2y + 12xy) + (20xz + 5z)
12xy(48x^2y + 12xy) + 5z(20xz + 5z) [factor out the GCF amongst each group]

12xy(48x^2y/12xy + 12xy/12xy) + 5z(20xz/5z + 5z/5z) [divide each term by its GCF]
12xy(4x+1)+5z(4x+1) [re-factor out the next GCF ((4x+1)
(12xy+5z)(4x+1)

.
Check by multiplying the factors.  You should get the original expression.