Factor by grouping. \[ 4 x^{3}+3 x^{2}+20 x+15 \]

Step 1 ：Group the terms in pairs: (4x^3 + 3x^2) and (20x + 15).

Step 2 ：Factor out the greatest common factor (GCF) from each group: (4x + 3)*(x^2 + 5) and (4x + 3)*(x^2 + 5).

Step 3 ：The common factor in both groups is (4x + 3). Therefore, the factored form of the expression is (4x + 3)(x^2 + 5).

Step 4 ：Final Answer: \(\boxed{(4x + 3)(x^2 + 5)}\)