# 4/9w^2+1=5/3w solve by factoring

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Solve `4/9 w^2+1=5/3 w` :

`4/9 w^2-5/3 w+1=0` It is easier if you multiply through by 9 to clear the fractions:

`4w^2-15w+9=0` We seek two numbers whose product is 36 and whose sum is -15 -- the numbers are -12 and -3

`4w^2-3w-12w+9=0`

`w(4w-3)-3(4w-3)=0`

`(4w-3)(w-3)=0` Using the zero product property:

`4w-3=0 ==> w=3/4` and w-3=0 ==> w=3

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The two solutions are `w=3/4,w=3`

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change the improper fractions into whole numbers by multiplying everything by 9.

the function becomes

4w^2+9=15w

it now becomes easier to solve. Put everything on one side

4w^2-15w+9=0

4w^2-12w-3w+9=0

4w(w-3)-3(w-3)=0

(4w-3)(w-3)=0

therefore w=3 and w=3/4