Factor the following trinomial. If it cannot be factored, indicate "Not Factorable".
\[
20 x^{2}-11 x-4
\]

Step 1 ：The given expression is a quadratic trinomial. To factorize it, we need to find two numbers such that their product is equal to the product of the coefficient of \(x^{2}\) (which is 20) and the constant term (which is -4), and their sum is equal to the coefficient of \(x\) (which is -11).

Step 2 ：So, we need to find two numbers \(a\) and \(b\) such that: \(a \cdot b = 20 \cdot -4 = -80\) and \(a + b = -11\).

Step 3 ：We can solve this problem by trying out different pairs of factors of -80 and checking which pair sums up to -11.

Step 4 ：The pair of numbers that satisfy the conditions are 5 and -16. That is, \(a = 5\) and \(b = -16\).

Step 5 ：Now, we can rewrite the middle term of the trinomial as the sum of \(5x\) and \(-16x\), and then factor by grouping.

Step 6 ：The trinomial \(20x^{2} - 11x - 4\) can be rewritten as \(20x^{2} + 5x - 16x - 4\).

Step 7 ：Now, we can factor by grouping. The first two terms \(20x^{2} + 5x\) have a common factor of \(5x\), and the last two terms \(-16x - 4\) have a common factor of -4.

Step 8 ：So, the expression becomes \(5x(4x + 1) - 4(4x + 1)\).

Step 9 ：Now, we can factor out the common binomial \(4x + 1\), and the expression becomes \((5x - 4)(4x + 1)\).

Step 10 ：So, the factorization of the trinomial \(20x^{2} - 11x - 4\) is \((5x - 4)(4x + 1)\).

Step 11 ：Final Answer: The factorization of the trinomial \(20x^{2} - 11x - 4\) is \(\boxed{(5x - 4)(4x + 1)}\).