We're dividing 15965 by 42 
Let's see how many times 42 fits into 15965.

Let's proceed to step 1:
42 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 42

Moving on to step 2:
42 can be fit into 15 0 times, resulting in a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Bring next digit (9) of the dividend behind the 15 and repeat the process: 159 / 42

Advancing to step 3:
If we divide 159 by 42, we get 3 and a remainder of 33.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 126 away from 159, we end up with 33.
Bring next digit (6) of the dividend behind the 33 and repeat the process: 336 / 42

On to step 4:
When dividing 336 by 42, we get 8 with a remainder of 0.
The next digit of our result is 8. 
Result so far: 38.0
Deduct 336 from 336 and we're left with 0.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 42

Let's proceed to step 5:
42 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 380.0
Subtract 0 from 5 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 6:
When dividing 50 by 42, we get 1 with a remainder of 8.
Write down 1 as next digit of the result. 
Result so far: 380.1
Subtracting 42 from 50 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 7:
80 divided by 42 is 1 with a remainder of 38.
Use 1 as the next digit of our solution. 
Result so far: 380.11
If we take 42 away from 80, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The final result is 380.11 with a remainder of 0.038.