# Problem of the Week

## Updated at Sep 26, 2022 11:58 AM

This week we have another equation problem:

How would you solve the equation $$y(4y+2)=72$$?

Let's start!

$y(4y+2)=72$

 1 Expand.$4{y}^{2}+2y=72$2 Move all terms to one side.$4{y}^{2}+2y-72=0$3 Factor out the common term $$2$$.$2(2{y}^{2}+y-36)=0$4 Split the second term in $$2{y}^{2}+y-36$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -36=-72$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-72$$?$$9$$ and $$-8$$3 Split $$y$$ as the sum of $$9y$$ and $$-8y$$.$2{y}^{2}+9y-8y-36$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(2{y}^{2}+9y-8y-36)=0$5 Factor out common terms in the first two terms, then in the last two terms.$2(y(2y+9)-4(2y+9))=0$6 Factor out the common term $$2y+9$$.$2(2y+9)(y-4)=0$7 Solve for $$y$$.1 Ask: When will $$(2y+9)(y-4)$$ equal zero?When $$2y+9=0$$ or $$y-4=0$$2 Solve each of the 2 equations above.$y=-\frac{9}{2},4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=-\frac{9}{2},4$DoneDecimal Form: -4.5, 4y=-9/2,4