To solve the equation \( 4(5y + 3) - 5(3y + 1) = 27 \), we start by expanding both sides of the equation.
First, we distribute the \( 4 \) and \( -5 \):
\[ 4(5y + 3) = 20y + 12 \] \[ -5(3y + 1) = -15y - 5 \]
Now, substituting these back into the equation gives:
\[ 20y + 12 - 15y - 5 = 27 \]
Next, we combine like terms on the left-hand side:
\[ (20y - 15y) + (12 - 5) = 27 \] \[ 5y + 7 = 27 \]
Now, we isolate \( y \) by first subtracting \( 7 \) from both sides:
\[ 5y = 27 - 7 \] \[ 5y = 20 \]
Now, divide both sides by \( 5 \):
\[ y = \frac{20}{5} \] \[ y = 4 \]
Thus, the solution to the equation is \( y = 4 \).