# Math Help - This equation has two roots

1. ## This equation has two roots

3x^(6)e^(-2x)-9x^(7)e^(-2x)=0 has two roots

Where do I even start?

2. ## Re: This equation has two roots

I would start by dividing through by any non-zero numbers that are common to both sides of the equation. (I presume you know that $e^x$ is not 0 for ny x.)

3. ## Re: This equation has two roots

Originally Posted by RD33
3x^(6)e^(-2x)-9x^(7)e^(-2x)=0 has two roots
Where do I even start?
Factor it: $3x^6e^{-2x}(1-3x)=0~.$

4. ## Re: This equation has two roots

Ok I got the answer 0 and 1/3 but how did you factor it. Where does the (1-3x) come from?

5. ## Re: This equation has two roots

Originally Posted by RD33
Ok I got the answer 0 and 1/3 but how did you factor it. Where does the (1-3x) come from?
Can you factor $3a^6b-9a^7b~?$ What do you get?