We look at the division of 414129 by 6 
We're looking to find how many times 6 goes into 414129.

Going ahead to step 1:
If we divide 4 by 6, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 6

Advancing to step 2:
41 divided by 6 is 6 with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 36 from 41 to get 5.
Fetch the next digit (4) from the dividend, attach it to 5 and continue: 54 / 6

Moving on to step 3:
6 goes into 54 9 times with a remainder of 0.
Use 9 as the next digit of our solution. 
Result so far: 69.0
Subtract 54 from 54 to get 0.
Fetch the next digit (1) from the dividend, attach it to 0 and continue: 1 / 6

Step 4:
If we divide 1 by 6, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 690.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 6

Let's proceed to step 5:
6 goes into 12 2 times with a remainder of 0.
Record the quotient 2 as the next digit in the result. 
Result so far: 6902.0
Subtract 12 from 12 to get 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 6

Moving on to step 6:
6 can be fit into 9 1 times, resulting in a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 69021.0
If we take 6 away from 9, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 7:
30 divided by 6 is 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 69021.5
The remainder is 0 after subtracting 30 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 8:
0 divided by 6 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 69021.5
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.

Let's proceed to step 9:
6 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 69021.5
If we subtract 0 from 0, we 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.

The final outcome is 69021.5, with a leftover of 0.0.