Answer
$y=-5$ or $y=4$
Work Step by Step
$ y(y+9)=4(2y+5)\qquad$...apply the distributive rule: $m(n\pm c)=mn\pm mc$
$ y^{2}+9y=8y+20\qquad$...add $(-8y-20)$ to both sides
$y^{2}+y-20=0$
... Searching for two factors of $ac=-20$ whose sum is $b=1,$
we find$\qquad 5$ and $-4.$
Rewrite the middle term and factor in pairs:
$y^{2}+5y-4y-20=0$
$y(y+5)-4(y+5)=0$
$(y+5)(y-4)=0\qquad$...apply the principle of zero products.
$y+5=0$ or $y-4=0$
$y=-5$ or $y=4$
Type the equation into a graphing utility and see
that the graph intercepts the x-axis at $-5$ and $4$.
