\[ (5 y+2)(y+3)=6 y \] INSTRUCTION: Give your answers as simplified fractions. Answer: \( y=\square \) or \( y=\square \)

To solve the equation \( (5y + 2)(y + 3) = 6y \), we first expand the left side: \[ 5y^2 + 15y + 2y + 6 = 6y \] This simplifies to: \[ 5y^2 + 17y + 6 = 6y \] Next, we rearrange the equation to set it to zero: \[ 5y^2 + 17y - 6y + 6 = 0 \quad \Rightarrow \quad 5y^2 + 11y + 6 = 0 \] Now, we can factor the quadratic equation: \[ (5y + 3)(y + 2) = 0 \] Setting each factor to zero gives: \[ 5y + 3 = 0 \quad \Rightarrow \quad y = -\frac{3}{5} \] and \[ y + 2 = 0 \quad \Rightarrow \quad y = -2 \] Thus, the solutions are: \[ y = -\frac{3}{5} \quad \text{or} \quad y = -2 \]