Let's solve the equation step by step.
The given equation is: \[ 4x = 3(x + 5) - 15 \]
First, distribute the \(3\) on the right side: \[ 4x = 3x + 15 - 15 \]
This simplifies to: \[ 4x = 3x \]
Next, we can subtract \(3x\) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]
Now we check whether this solution is valid.
Since we derived a single value for \(x\) (which is \(0\)), we conclude that the equation has one solution.
Thus, the correct response is: The equation has one solution: x = 0.