Consider $\left(y+3\right)\left(y-3\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $3$.
$$y^{2}-9-y\left(y+5\right)=6$$
Use the distributive property to multiply $y$ by $y+5$.
$$y^{2}-9-\left(y^{2}+5y\right)=6$$
To find the opposite of $y^{2}+5y$, find the opposite of each term.