To factorize the expression (4x+3)(x+9), we can use the distributive property of multiplication:
(4x+3)(x+9) = 4x(x+9) + 3(x+9)
Now we can factor out the common factor of (x+9):
4x(x+9) + 3(x+9) = (4x+3)(x+9)
Therefore, the factored form of the expression (4x+3)(x+9) is (4x+3)(x+9).