algebra
posted by SO LOST .
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}

First of all, x=0 is clearly a solution.
For other solutions, divide both sides by x to get the quadratic
(x+6)(x4) = 24
x^2 +2x 24 = 24
x^2 +2x 48 = 0
(x+8)(x6) = 0
x = 8 or 6
Your answer is correct but you got there the hard way.