We're dividing 87259 by 84 
Our goal is to divide 87259 by 84.

Advancing to step 1:
8 divided by 84 is 0 with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Fetch the next digit (7) from the dividend, attach it to 8 and continue: 87 / 84

Step 2:
When dividing 87 by 84, we get 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 84 from 87, we get 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 84

Step 3:
32 divided by 84 is 0 with a remainder of 32.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 32 after subtracting 0 from 32.
Append the next digit (5) from the dividend to 32 and continue with: 325 / 84

Moving on to step 4:
If we divide 325 by 84, we get 3 and a remainder of 73.
The number 3 becomes the next digit in our result. 
Result so far: 103.0
If we take 252 away from 325, we end up with 73.
Take the next digit (9) from the dividend and append it to 73, then repeat: 739 / 84

Going ahead to step 5:
When dividing 739 by 84, we get 8 with a remainder of 67.
Use 8 as the next digit of our solution. 
Result so far: 1038.0
Deduct 672 from 739 and we're left with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Let's proceed to step 6:
The number 84 fits into 670 7 times, leaving a remainder of 82.
Put 7 as the next digit of the answer. 
Result so far: 1038.7
Subtracting 588 from 670 leaves us with 82.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Moving on to step 7:
The number 84 fits into 820 9 times, leaving a remainder of 64.
Record the quotient 9 as the next digit in the result. 
Result so far: 1038.79
Subtract 756 from 820 to get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Advancing to step 8:
The number 84 fits into 640 7 times, leaving a remainder of 52.
The next digit of our result is 7. 
Result so far: 1038.797
If we take 588 away from 640, we end up with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Let's proceed to step 9:
520 divided by 84 is 6 with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 1038.7976
The remainder is 16 after subtracting 504 from 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 10:
84 can be fit into 160 1 times, resulting in a remainder of 76.
Put 1 as the next digit of the answer. 
Result so far: 1038.79761
Subtracting 84 from 160 leaves us with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Moving on to step 11:
84 can be fit into 760 9 times, resulting in a remainder of 4.
The next digit of our result is 9. 
Result so far: 1038.797619
The remainder is 4 after subtracting 756 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 12:
84 can be fit into 40 0 times, resulting in a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 1038.797619
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 13:
If we divide 400 by 84, we get 4 and a remainder of 64.
Record the quotient 4 as the next digit in the result. 
Result so far: 1038.79761904
If we take 336 away from 400, we end up with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

In conclusion, the division gives 1038.79761904 with a balance of 6.4e-08.