To solve the equation \( 4(2x + 1) = 27 + 3(2x - 5) \), let's first expand both sides.
Start with the left side:
\[ 4(2x + 1) = 8x + 4 \]
Now expand the right side:
\[ 3(2x - 5) = 6x - 15 \]
Then, we rewrite the right side:
\[ 27 + 3(2x - 5) = 27 + 6x - 15 = 6x + 12 \]
Now we have the equation:
\[ 8x + 4 = 6x + 12 \]
Next, we can isolate \( x \) by subtracting \( 6x \) from both sides:
\[ 8x - 6x + 4 = 12 \]
This simplifies to:
\[ 2x + 4 = 12 \]
Next, subtract 4 from both sides:
\[ 2x = 12 - 4 \] \[ 2x = 8 \]
Now, divide both sides by 2:
\[ x = \frac{8}{2} = 4 \]
Thus, the value of \( x \) is:
\[ \boxed{4} \]