2x^3-8x^2-24x=2x(ax+b)(cx+d)

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Solution for 2x^3-8x^2-24x=2x(ax+b)(cx+d) equation: 


Simplifying
2x3 + -8x2 + -24x = 2x(ax + b)(cx + d)

Reorder the terms:
-24x + -8x2 + 2x3 = 2x(ax + b)(cx + d)

Multiply (ax + b) * (cx + d)
-24x + -8x2 + 2x3 = 2x(ax(cx + d) + b(cx + d))
-24x + -8x2 + 2x3 = 2x((cx * ax + d * ax) + b(cx + d))
-24x + -8x2 + 2x3 = 2x((acx2 + adx) + b(cx + d))
-24x + -8x2 + 2x3 = 2x(acx2 + adx + (cx * b + d * b))
-24x + -8x2 + 2x3 = 2x(acx2 + adx + (bcx + bd))
-24x + -8x2 + 2x3 = 2x(acx2 + adx + bcx + bd)
-24x + -8x2 + 2x3 = (acx2 * 2x + adx * 2x + bcx * 2x + bd * 2x)
-24x + -8x2 + 2x3 = (2acx3 + 2adx2 + 2bcx2 + 2bdx)

Solving
-24x + -8x2 + 2x3 = 2acx3 + 2adx2 + 2bcx2 + 2bdx

Solving for variable 'x'.

Reorder the terms:
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 2acx3 + 2adx2 + 2bcx2 + 2bdx + -2acx3 + -2adx2 + -2bcx2 + -2bdx

Reorder the terms:
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 2acx3 + -2acx3 + 2adx2 + -2adx2 + 2bcx2 + -2bcx2 + 2bdx + -2bdx

Combine like terms: 2acx3 + -2acx3 = 0
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 0 + 2adx2 + -2adx2 + 2bcx2 + -2bcx2 + 2bdx + -2bdx
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 2adx2 + -2adx2 + 2bcx2 + -2bcx2 + 2bdx + -2bdx

Combine like terms: 2adx2 + -2adx2 = 0
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 0 + 2bcx2 + -2bcx2 + 2bdx + -2bdx
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 2bcx2 + -2bcx2 + 2bdx + -2bdx

Combine like terms: 2bcx2 + -2bcx2 = 0
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 0 + 2bdx + -2bdx
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 2bdx + -2bdx

Combine like terms: 2bdx + -2bdx = 0
-2acx3 + -2adx2 + -2bcx2 + -2bdx + -24x + -8x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1acx2 + -1adx + -1bcx + -1bd + -12 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-1acx2 + -1adx + -1bcx + -1bd + -12 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-1acx2 + -1adx + -1bcx + -1bd + -12 + -4x + x2 = 0

Reorder the terms:
-12 + -1acx2 + -1adx + -1bcx + -1bd + -4x + x2 = 0

Solving
-12 + -1acx2 + -1adx + -1bcx + -1bd + -4x + x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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