We look at the division of 129415 by 3 
We're looking to find how many times 3 goes into 129415.

Going ahead to step 1:
The number 3 fits into 1 0 times, leaving 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.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 3

Moving on to step 2:
12 divided by 3 is 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 4.0
Subtracting 12 from 12 leaves us with 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 3

On to step 3:
9 divided by 3 is 3 with a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 43.0
The remainder is 0 after subtracting 9 from 9.
Take the next digit (4) from the dividend and append it to 0, then repeat: 4 / 3

Let's proceed to step 4:
When dividing 4 by 3, we get 1 with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 431.0
Deduct 3 from 4 and we're left with 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 3

Let's proceed to step 5:
3 goes into 11 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 4313.0
Deduct 9 from 11 and we're left with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 3

Advancing to step 6:
When dividing 25 by 3, we get 8 with a remainder of 1.
Use 8 as the next digit of our solution. 
Result so far: 43138.0
Subtracting 24 from 25 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
The number 3 fits into 10 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 43138.3
If we take 9 away from 10, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 8:
3 goes into 10 3 times with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 43138.33
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 43138.33 and a remainder of 0.001.