Solve by factoring: `30x^3 = 21x^2 + 135x`

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Solve by factoring: `30x^3= 21x^2+135x`

First group everything on one side and then factorize as we have a common factor of 3x:

`30x^3-21x^2- 135x = 0`

`therefore 3x(10x^2-7x-45) =0`

`therefore 3x=0`         and   `10x^2-7x-45=0`     

`therefore x=0`             and `(5x+9)(2x-5)=0` .

Note that we factorized by using appropriate factors from the first term`(5x times2x)`  and the third term `(+9 times -5)` which renders a middle term of `-7`

 Now solve each of those factors:

`therefore 5x+9=0`       and     `2x-5=0`

`therefore 5x=-9`         and    `2x=5`

`therefore x=-9/5`            and     `x=5/2`  

Ans: x=0; x=`-9/5`   and x= `5/2`