Help with maths please, yr 10 level - Null Factor Law?

Question

-3x^2 - 9x = 0

Null Factor Law

PLEASE HELP!

Answer 1

First, pull out an x on the left:

x(-3x - 9) = 0

Now, if the product of two things is zero, then one of those things must itself be zero. So:

Either x = 0, OR -3x - 9 = 0

Let's solve the second equation:

-3x - 9 = 0

-3x = 9

x = -3.

So x = 0 and x = -3 are the solutions.

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You can check this answer to see that it's reasonable:

-3(0)^2 - 9(0) = 0. This checks out.

-3(-3)^2 - 9(-3) = (-3)(9) - (-27) = (-27) - (-27) = 0. So this checks out also.

Answer 2

Factor out an x.

(-3x - 9)x = 0

Because the only way for ab to equal 0 is for a or b to equal 0:

x = 0

-3x - 9 = 0

-3x = 9

x = -3

So x = 0, x = -3