# Problem of the Week

## Updated at Dec 16, 2019 5:03 PM

This week we have another equation problem:

How can we solve the equation $$\frac{25({y}^{2}-3)}{y}=-50$$?

Let's start!

$\frac{25({y}^{2}-3)}{y}=-50$

 1 Multiply both sides by $$y$$.$25({y}^{2}-3)=-50y$2 Divide both sides by $$25$$.${y}^{2}-3=-2y$3 Move all terms to one side.${y}^{2}-3+2y=0$4 Factor $${y}^{2}-3+2y$$.1 Ask: Which two numbers add up to $$2$$ and multiply to $$-3$$?$$-1$$ and $$3$$2 Rewrite the expression using the above.$(y-1)(y+3)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$(y-1)(y+3)=0$5 Solve for $$y$$.1 Ask: When will $$(y-1)(y+3)$$ equal zero?When $$y-1=0$$ or $$y+3=0$$2 Solve each of the 2 equations above.$y=1,-3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=1,-3$Doney=1,-3