To solve this equation, we need to find the value of x.

First, let's simplify the expression inside the parentheses:

(-100 + 99 - 98 + ... - 2 + 1)

We can see that there is a pattern of subtracting consecutive numbers, so we can rewrite this expression as:

(-100 - 98 - 96 - ... - 2) + (99 + 97 + 95 + ... + 1)

The first part of the expression is a sum of an arithmetic series with a common difference of -2. We can use the formula for the sum of an arithmetic series to find its value:

Sum = (n/2)(first term + last term)

In this case, the first term is -100 and the last term is -2. The number of terms, n, can be found by dividing the difference between the first and last term by the common difference and adding 1:

n = (-2 - (-100)) / -2 + 1
= (-2 + 100) / -2 + 1
= 98 / -2 + 1
= -49 + 1
= -48

So, the sum of the first part of the expression is:

(-48/2)(-100 + -2)
= (-24)(-102)
= 2448

The second part of the expression is a sum of an arithmetic series with a common difference of 2. Using the same formula, we can find its value:

Sum = (n/2)(first term + last term)

In this case, the first term is 99 and the last term is 1. The number of terms, n, can be found by dividing the difference between the first and last term by the common difference and adding 1:

n = (1 - 99) / 2 + 1
= (-98) / 2 + 1
= -49 + 1
= -48

So, the sum of the second part of the expression is:

(-48/2)(99 + 1)
= (-24)(100)
= -2400

Now, let's substitute these values back into the original equation:

2448 - 2400 - x = 15

Simplifying further:

48 - x = 15

To isolate x, we can subtract 48 from both sides:

-x = 15 - 48
x = -33

Therefore, the value of x is -33.