Answer
$y=-2$.
Work Step by Step
The given equation is
$\Rightarrow 9(y-4)-7y=5(3y-2)$
Use distributive property.
$\Rightarrow 9y-36-7y=15y-10$
Add like terms.
$\Rightarrow 2y-36=15y-10$
Add $10$ to both sides.
$\Rightarrow 2y-36+10=15y-10+10$
Simplify.
$\Rightarrow 2y-26=15y$
Subtract $2y$ from both sides.
$\Rightarrow 2y-26-2y=15y-2y$
Simplify.
$\Rightarrow -26=13y$
Divide both sides by $13$.
$\Rightarrow \frac{-26}{13}=\frac{13y}{13}$
Simplify.
$\Rightarrow -2=y$
Check :-
$\Rightarrow 9(-2-4)-7(-2)=5(3(-2)-2)$
$\Rightarrow 9(-6)+14=5(-6-2)$
$\Rightarrow 9(-6)+14=5(-8)$
$\Rightarrow -54+14=-40$
$\Rightarrow -40=-40$
True.
Hence, the solution is $y=-2$.
