We're dividing 431742 by 75 
We want to divide 431742 by 75.

Let's proceed to step 1:
75 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 75

Going ahead to step 2:
75 goes into 43 0 times with a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 43, we get 43.
Append the next digit (1) from the dividend to 43 and continue with: 431 / 75

On to step 3:
75 goes into 431 5 times with a remainder of 56.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Deduct 375 from 431 and we're left with 56.
Include the next digit (7) from the dividend after 56, then repeat: 567 / 75

Step 4:
75 goes into 567 7 times with a remainder of 42.
The number 7 becomes the next digit in our result. 
Result so far: 57.0
If we subtract 525 from 567, we get 42.
Bring next digit (4) of the dividend behind the 42 and repeat the process: 424 / 75

On to step 5:
The number 75 fits into 424 5 times, leaving a remainder of 49.
The next digit of our result is 5. 
Result so far: 575.0
If we subtract 375 from 424, we get 49.
Take the next digit (2) from the dividend and append it to 49, then repeat: 492 / 75

Step 6:
492 divided by 75 is 6 with a remainder of 42.
Use 6 as the next digit of our solution. 
Result so far: 5756.0
The remainder is 42 after subtracting 450 from 492.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 7:
420 divided by 75 is 5 with a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 5756.5
The remainder is 45 after subtracting 375 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 8:
75 goes into 450 6 times with a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 5756.56
Subtract 450 from 450 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 9:
The number 75 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 5756.56
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 10:
75 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 5756.56
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 5756.56 with a balance of 0.0.