Variable $y$ cannot be equal to $-\frac{9}{5}$ since division by zero is not defined. Multiply both sides of the equation by $5\left(5y+9\right)$, the least common multiple of $1\times 5y+9,5$.
$$5\left(0.4y-3\right)=-7\left(5y+9\right)$$
Use the distributive property to multiply $5$ by $0.4y-3$.
$$2y-15=-7\left(5y+9\right)$$
Use the distributive property to multiply $-7$ by $5y+9$.
$$2y-15=-35y-63$$
Add $35y$ to both sides.
$$2y-15+35y=-63$$
Combine $2y$ and $35y$ to get $37y$.
$$37y-15=-63$$
Add $15$ to both sides.
$$37y=-63+15$$
Add $-63$ and $15$ to get $-48$.
$$37y=-48$$
Divide both sides by $37$.
$$y=\frac{-48}{37}$$
Fraction $\frac{-48}{37}$ can be rewritten as $-\frac{48}{37}$ by extracting the negative sign.
