Posted by **SO LOST** on Wednesday, February 2, 2011 at 12:35pm.

Did I do this problem the correct way if so is there a shorter way to explain this?

x(x + 6)(x + -4) = 24x

x(6 + x)(x + -4) = 24x

x(6 + x)(-4 + x) = 24x

(6 + x) * (-4 + x

x(6(-4 + x) + x(-4 + x)) = 24x

x((-4 * 6 + x * 6) + x(-4 + x)) = 24x

x((-24 + 6x) + x(-4 + x)) = 24x

x(-24 + 6x + (-4 * x + x * x)) = 24x

x(-24 + 6x + (-4x + x2)) = 24x

6x + -4x = 2x

x(-24 + 2x + x2) = 24x

(-24 * x + 2x * x + x2 * x) = 24x

(-24x + 2x2 + x3) = 24x

-24x + 2x2 + x3 = 24x

-24x + -24x + 2x2 + x3 = 24x + -24x

-24x + -24x = -48x

-48x + 2x2 + x3 = 24x + -24x

24x + -24x = 0

-48x + 2x2 + x3 = 0

x(-48 + 2x + x2) = 0

x((-8 + -1x)(6 + -1x)) = 0

x = 0

-8 + 8 + -1x = 0 + 8

0 + -1x = 0 + 8

-1x = 0 + 8

-1x = 8

x = -8

x = {0, -8, 6}

- algebra -
**drwls**, Wednesday, February 2, 2011 at 12:43pm
First of all, x=0 is clearly a solution.

For other solutions, divide both sides by x to get the quadratic

(x+6)(x-4) = 24

x^2 +2x -24 = 24

x^2 +2x -48 = 0

(x+8)(x-6) = 0

x = -8 or 6

Your answer is correct but you got there the hard way.

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