We're dividing 421314 by 84 
We want to figure out the number of times 421314 can be divided by 84.

Let's proceed to step 1:
84 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 84

Moving on to step 2:
84 can be fit into 42 0 times, resulting in a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Include the next digit (1) from the dividend after 42, then repeat: 421 / 84

Step 3:
When dividing 421 by 84, we get 5 with a remainder of 1.
Put 5 as the next digit of the answer. 
Result so far: 5.0
If we subtract 420 from 421, we get 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 84

Step 4:
The number 84 fits into 13 0 times, leaving a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 50.0
If we take 0 away from 13, we end up with 13.
Bring next digit (1) of the dividend behind the 13 and repeat the process: 131 / 84

Advancing to step 5:
If we divide 131 by 84, we get 1 and a remainder of 47.
The next digit of our result is 1. 
Result so far: 501.0
The remainder is 47 after subtracting 84 from 131.
Append the next digit (4) from the dividend to 47 and continue with: 474 / 84

Moving on to step 6:
The number 84 fits into 474 5 times, leaving a remainder of 54.
The next digit of our result is 5. 
Result so far: 5015.0
If we take 420 away from 474, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Let's proceed to step 7:
When dividing 540 by 84, we get 6 with a remainder of 36.
The number 6 becomes the next digit in our result. 
Result so far: 5015.6
The remainder is 36 after subtracting 504 from 540.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 8:
84 can be fit into 360 4 times, resulting in a remainder of 24.
Use 4 as the next digit of our solution. 
Result so far: 5015.64
If we subtract 336 from 360, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 9:
84 can be fit into 240 2 times, resulting in a remainder of 72.
The number 2 becomes the next digit in our result. 
Result so far: 5015.642
Deduct 168 from 240 and we're left with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Moving on to step 10:
When dividing 720 by 84, we get 8 with a remainder of 48.
The next digit of our result is 8. 
Result so far: 5015.6428
If we take 672 away from 720, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 11:
When dividing 480 by 84, we get 5 with a remainder of 60.
The number 5 becomes the next digit in our result. 
Result so far: 5015.64285
If we subtract 420 from 480, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 12:
84 goes into 600 7 times with a remainder of 12.
Record the quotient 7 as the next digit in the result. 
Result so far: 5015.642857
If we subtract 588 from 600, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 13:
When dividing 120 by 84, we get 1 with a remainder of 36.
Put 1 as the next digit of the answer. 
Result so far: 5015.6428571
The remainder is 36 after subtracting 84 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 14:
84 can be fit into 360 4 times, resulting in a remainder of 24.
The next digit of our result is 4. 
Result so far: 5015.64285714
Deduct 336 from 360 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

In conclusion, the division gives 5015.64285714 with a balance of 2.4e-08.