# Chapter: Solving quadratic equations by factorization.  Question: The length and breadth of a rectangle are (3y+1)cm and (2y-1)cm respectively. If the are of the rectangle is 144cm2, find the value of y.  Please help, urgent!

The area is length times breadth. Substituting the known values we get:

144=(3y+1)(2y-1)    Multiply the binomials:

`6y^2-y-1=144`

`6y^2-y-145=0`

There are a number of methods to factor the left side, if it factors. One way is to find a pair of numbers whose product is (6)(-145)=-870 and whose sum is -1. The numbers are 29 and -30. Then we can rewrite the trinomial as:

`6y^2-30y+29y-145=0`  Factor two terms at a time:

`6y(y-5)+29(y-5)=0` Use the distributive property:

`(y-5)(6y+29)=0`  Now use the zero product property:

y-5=0 ==> y=5

6y+29=0 ==> `y=-29/6` . If y<0 then 3y+1<0 so this cannot be an answer since a length must be positive.

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The solution is y=5

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Check: (3(5)+1)(2(5)-1)=(16)(9)=144 as required.

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