-3(x + 12) - 2(x - 18) = -5x

To solve the equation \(-3(x + 12) - 2(x - 18) = -5x\), we will first distribute the terms on the left side:

1. Distribute \(-3\) in \(-3(x + 12)\): \[ -3x - 36 \]

2. Distribute \(-2\) in \(-2(x - 18)\): \[ -2x + 36 \]

Now, combine these results: \[ -3x - 36 - 2x + 36 = -5x \]

Next, combine like terms on the left side: \[ (-3x - 2x) + (-36 + 36) = -5x \] \[ -5x + 0 = -5x \]

This simplifies to: \[ -5x = -5x \]

Since this is true for all \(x\), it means the equation is an identity. Therefore, the solution is that there are infinitely many solutions for \(x\).