To solve the equation \( 4x = 3 (x + 5) - 15 \), we will first simplify the right side.
Starting with the equation: \[ 4x = 3(x + 5) - 15 \]
Distributing \(3\) on the right side: \[ 4x = 3x + 15 - 15 \]
This simplifies to: \[ 4x = 3x \]
Next, we will subtract \(3x\) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]
Now, we will check if this solution is valid by substituting \(x = 0\) back into the original equation: \[ 4(0) = 3(0 + 5) - 15 \] \[ 0 = 15 - 15 \] \[ 0 = 0 \]
Since both sides of the equation are equal, the solution \(x = 0\) is valid.
Conclusion: The equation has one unique solution, \(x = 0\).