Factor. \[ 3 x^{2}+19 x+30 \]

Step 1 ：The given expression is a quadratic equation of the form \(ax^2 + bx + c\).

Step 2 ：To factorize it, we need to find two numbers such that their sum is equal to the coefficient of x (which is 19 in this case) and their product is equal to the constant term (which is 30 in this case).

Step 3 ：The factored form of the given quadratic equation is \((x + 3)*(3*x + 10)\)

Step 4 ：\(\boxed{(x + 3)*(3*x + 10)}\) is the final answer.