Factorise 20x2+41x+20 completely.

Sure, here is the step-by-step solution:

Step 1: Identify the coefficients of the quadratic equation. In this case, a = 20, b = 41, and c = 20.

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 20*20 = 400 and b = 41. The numbers are 16 and 25.

Step 3: Rewrite the middle term (41x) as the sum of the terms 16x and 25x. This gives us: 20x^2 + 16x + 25x + 20.

Step 4: Factor by grouping. This involves factoring out the greatest common factor (GCF) from each of the two groups:

20x^2 + 16x + 25x + 20 = 4x(5x + 4) + 5(5x + 4)

Step 5: Notice that (5x + 4) is a common factor. Factor this out to give the final answer:

4x(5x + 4) + 5(5x + 4) = (5x + 4)(4x + 5)

So, 20x^2 + 41x + 20 completely factorises to (5x + 4)(4x + 5).