Variable $y$ cannot be equal to $\frac{5}{3}$ since division by zero is not defined. Multiply both sides of the equation by $7\left(3y-5\right)$, the least common multiple of $3y-5,7$.
$$7\left(2y+1\right)=4\left(3y-5\right)$$
Use the distributive property to multiply $7$ by $2y+1$.
$$14y+7=4\left(3y-5\right)$$
Use the distributive property to multiply $4$ by $3y-5$.
$$14y+7=12y-20$$
Subtract $12y$ from both sides.
$$14y+7-12y=-20$$
Combine $14y$ and $-12y$ to get $2y$.
$$2y+7=-20$$
Subtract $7$ from both sides.
$$2y=-20-7$$
Subtract $7$ from $-20$ to get $-27$.
$$2y=-27$$
Divide both sides by $2$.
$$y=\frac{-27}{2}$$
Fraction $\frac{-27}{2}$ can be rewritten as $-\frac{27}{2}$ by extracting the negative sign.
