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.
\[2(2{y}^{2}+9y-8y-36)=0\]

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 \(y\).
\[y=-\frac{9}{2},4\]

Done

Decimal Form: -4.5, 4
Cymath foriOSAndroid