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1. my mind's gone blank and i can't seem to solve this basic equation through factorising- anyone know what i need to do?

3x2 + 5x = 0
2. There is an x common in both terms.
So we can say .
3. (Original post by entertainmyfaith)
my mind's gone blank and i can't seem to solve this basic equation through factorising- anyone know what i need to do?

3x2 + 5x = 0
common factor of x

factorise -> x(3x + 5) = 0

so x = 0 or x = -5/3
4. (Original post by DrDyk)
common factor of x

factorise -> x(3x + 5) = 0

so x = 0 or x = -5/3
i'm sorry how did you get -5/3? it's not wrong because i've checked the textbook answer i just can't work out how you got it
5. (Original post by entertainmyfaith)
i'm sorry how did you get -5/3? it's not wrong because i've checked the textbook answer i just can't work out how you got it
So in order to get ' (x)(3x + 5) ' equal to 0, one of the brackets (you can imagine brackets around the x on its own) has to be equal to zero. Anything multiplied by 0 is 0.

so, if x = 0, the first bracket is 0 and the whole equation must equal 0.

if x = -5/3, the second bracket is 0 and so the whole equation must equal 0.

You can work out the second bracket by putting 3x+ 5 = 0

3x+5 = 0 -> 3x = -5 -> x = -5/3

Hope this helps
6. When you have the following equation:

For this to be true, either x = 0 or the inside of the brackets must equal zero, as something multiplied by zero equals zero.

So now ask, "what does x need to be for the inside of the brackets to equal zero?", we can do that trivially by rearranging the equation:

3x + 5 = 0
3x = -5
x =(-5/3)

This makes sense, as multiplying -5/3 by three gives -5, and -5 + 5 equals zero.
7. (Original post by entertainmyfaith)
i'm sorry how did you get -5/3? it's not wrong because i've checked the textbook answer i just can't work out how you got it
If then either or . You can solve the latter to get your second solution Does this make sense?
8. (Original post by DrDyk)
So in order to get ' (x)(3x + 5) ' equal to 0, one of the brackets (you can imagine brackets around the x on its own) has to be equal to zero. Anything multiplied by 0 is 0.

so, if x = 0, the first bracket is 0 and the whole equation must equal 0.

if x = -5/3, the second bracket is 0 and so the whole equation must equal 0.

You can work out the second bracket by putting 3x+ 5 = 0

3x+5 = 0 -> 3x = -5 -> x = -5/3

Hope this helps
ah that makes sense thank you!
9. (Original post by entertainmyfaith)
ah that makes sense thank you!
Graph of 3x2 + 5x = 0

Hopefully you can see, when x = 0 and x = -5/3, the y value of the corresponding graph is 0. This is why there are two solutions for when this equation equals 0.

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