-7x - 12 = (fill in the blank)x + 12

To solve for the value that fills in the blank in the equation \(-7x - 12 = (fill in the blank)x + 12\), we can rearrange the equation:

1. Rewrite it as:
\[
-7x - 12 = bx + 12
\]

where \(b\) is the value that we need to find.

2. Add \(12\) to both sides:
\[
-7x - 12 + 12 = bx + 12 + 12
\]
Simplifying it gives:
\[
-7x = bx + 24
\]

3. Now, let's isolate \(x\):
\[
-7x - bx = 24
\]
Factoring out \(x\),
\[
(-7 - b)x = 24
\]

4. For this equation to hold true for all \(x\), the coefficient of \(x\) on the left (i.e., \(-7 - b\)) must equal \(0\). Therefore, we can set up the equation:
\[
-7 - b = 0
\]

5. Solving for \(b\):
\[
b = -7
\]

Thus, the filled-in blank would be \(-7\). Therefore, the equation can be completed as:
\[
-7x - 12 = -7x + 12
\]