Factorise 40x2+37x+4 completely.

Sure, here is the step-by-step solution to factorize the given quadratic equation 40x^2 + 37x + 4.

Step 1: Multiply the coefficient of x^2 (which is 40) with the constant term (which is 4). So, 40 * 4 = 160.

Step 2: Now, we need to find two numbers that multiply to 160 (from step 1) and add up to 37 (the coefficient of x). The numbers are 32 and 5 because 32 * 5 = 160 and 32 + 5 = 37.

Step 3: Rewrite the middle term of the quadratic equation (37x) as the sum of 32x and 5x. So, the equation becomes 40x^2 + 32x + 5x + 4.

Step 4: Factor by grouping. The first two terms can be grouped together and the last two terms can be grouped together. This gives us 8x(5x + 4) + 1(5x + 4).

Step 5: Now, you can see that (5x + 4) is a common factor. So, the fully factorized form of the equation is (8x + 1)(5x + 4).

So, 40x^2 + 37x + 4 = (8x + 1)(5x + 4).