We're dividing 421142 by 75 
We want to figure out the number of times 421142 can be divided by 75.

Advancing to step 1:
If we divide 4 by 75, we get 0 and a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 75

Going ahead to step 2:
75 can be fit into 42 0 times, resulting in a remainder of 42.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Append the next digit (1) from the dividend to 42 and continue with: 421 / 75

Moving on to step 3:
75 goes into 421 5 times with a remainder of 46.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Deduct 375 from 421 and we're left with 46.
Include the next digit (1) from the dividend after 46, then repeat: 461 / 75

On to step 4:
75 goes into 461 6 times with a remainder of 11.
Use 6 as the next digit of our solution. 
Result so far: 56.0
Deduct 450 from 461 and we're left with 11.
Include the next digit (4) from the dividend after 11, then repeat: 114 / 75

Moving on to step 5:
114 divided by 75 is 1 with a remainder of 39.
The next digit of our result is 1. 
Result so far: 561.0
If we take 75 away from 114, we end up with 39.
Fetch the next digit (2) from the dividend, attach it to 39 and continue: 392 / 75

Step 6:
75 goes into 392 5 times with a remainder of 17.
Put 5 as the next digit of the answer. 
Result so far: 5615.0
If we take 375 away from 392, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 7:
75 goes into 170 2 times with a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 5615.2
Deduct 150 from 170 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
75 goes into 200 2 times with a remainder of 50.
Write down 2 as next digit of the result. 
Result so far: 5615.22
Subtracting 150 from 200 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

After the division, we end up with 5615.22 and a remainder of 0.05.