Originally Posted by

**brianscherms** So when you have an equation such as x^2 + 4x + 9 = 0, and you're looking for the two x values where y = 0, you can use the quadratic equation or you can factor it out or simplify it... So forgetting the equation mentioned above and going to this one

-3x^2 + 12x = 0, I want to find the x values where this is true. I could... multiply the whole equation by (-1/3) which would give me...

x^2 -4 = 0. Then we can do x^2 = 4, and then square both sides which gives us... x = 2 and/or x = (-2). So this means that the two x points where y = 0 are x = 2 or x= -2...

What doesnt make sense to me is that you can also do...

-3x^2 + 12x = 0... and you can factor out the -3... which makes it... -3x(x - 4) = 0.. then you can do the thing where you split it and do

-3x = 0 and x - 4 = 0... so x = 0 and/or x = 4...

Mathematically I think I'm doing correct steps for both but I get different answers for x.

When should you do which method?