Variable $y$ cannot be equal to $-2$ since division by zero is not defined. Multiply both sides of the equation by $3\left(y+2\right)$, the least common multiple of $y+2,3$.
$$3\left(7y+4\right)=-4\left(y+2\right)$$
Use the distributive property to multiply $3$ by $7y+4$.
$$21y+12=-4\left(y+2\right)$$
Use the distributive property to multiply $-4$ by $y+2$.
$$21y+12=-4y-8$$
Add $4y$ to both sides.
$$21y+12+4y=-8$$
Combine $21y$ and $4y$ to get $25y$.
$$25y+12=-8$$
Subtract $12$ from both sides.
$$25y=-8-12$$
Subtract $12$ from $-8$ to get $-20$.
$$25y=-20$$
Divide both sides by $25$.
$$y=\frac{-20}{25}$$
Reduce the fraction $\frac{-20}{25}$ to lowest terms by extracting and canceling out $5$.
