Solve for x: 122400000 + 0.72x + 12x + 1020000 + 400000 + 0.13(122400000 - 1200x) = 1200x.

Step-by-step solution

1. 1

   Combine the $x$-terms that are already loose. On the left, $0.72x$ and $12x$ are like terms:

   $0.72x+12x=12.72x$

   Do this before touching the bracket — it keeps the bookkeeping short.

2. 2

   Add the plain constants. Still on the left, outside the bracket:

   $122400000+1020000+400000=123820000$

   The equation is now

   $123820000+12.72x+0.13(122400000-1200x)=1200x$

3. 3

   Distribute the 13%. The bracket contributes both a constant and an $x$-term:

   $0.13\times 122400000=15912000,\qquad 0.13\times 1200x=156x$

   so $0.13(122400000-1200x)=15912000-156x$. The minus sign belongs to the $x$-term, which is where sign slips usually happen.

4. 4

   Collect each kind of term once more.

   $123820000+15912000=139732000,\qquad 12.72x-156x=-143.28x$

   giving

   $139732000-143.28x=1200x$

5. 5

   Move every $x$ to the right. Adding $143.28x$ to both sides:

   $139732000=1200x+143.28x=1343.28x$

   Notice the coefficient is $1343.28$, not $1200$: the $-143.28x$ that came out of the bracket has to be carried across.

6. 6

   Divide and check.

   $x=\frac{139732000}{1343.28}=104022.9885\ldots$

   Substituting $x=104022.9885$ back gives $124827586.21$ on both sides, so

   $x\approx 104022.99$