To solve the equation \( 3(x + 4) + 5x = 4(x - 3) - 8x \), we will start by expanding both sides.
Step 1: Expand both sides.
Left side: \[ 3(x + 4) + 5x = 3x + 12 + 5x = 8x + 12 \]
Right side: \[ 4(x - 3) - 8x = 4x - 12 - 8x = -4x - 12 \]
Now we rewrite the equation:
\[ 8x + 12 = -4x - 12 \]
Step 2: Move all terms involving \(x\) to one side and constant terms to the other side.
Add \(4x\) to both sides: \[ 8x + 4x + 12 = -12 \] \[ 12x + 12 = -12 \]
Now subtract \(12\) from both sides: \[ 12x = -12 - 12 \] \[ 12x = -24 \]
Step 3: Solve for \(x\).
Divide both sides by \(12\): \[ x = \frac{-24}{12} = -2 \]
Thus, the solution to the equation is: \[ \boxed{-2} \]