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

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


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

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

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

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

Multiply (b + x) * (c + x)
-24x + -8x2 + 2x3 = ax(b(c + x) + x(c + x))
-24x + -8x2 + 2x3 = ax((c * b + x * b) + x(c + x))
-24x + -8x2 + 2x3 = ax((bc + bx) + x(c + x))
-24x + -8x2 + 2x3 = ax(bc + bx + (c * x + x * x))
-24x + -8x2 + 2x3 = ax(bc + bx + (cx + x2))
-24x + -8x2 + 2x3 = ax(bc + bx + cx + x2)
-24x + -8x2 + 2x3 = (bc * ax + bx * ax + cx * ax + x2 * ax)
-24x + -8x2 + 2x3 = (abcx + abx2 + acx2 + ax3)

Solving
-24x + -8x2 + 2x3 = abcx + abx2 + acx2 + ax3

Solving for variable 'x'.

Reorder the terms:
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = abcx + abx2 + acx2 + ax3 + -1abcx + -1abx2 + -1acx2 + -1ax3

Reorder the terms:
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = abcx + -1abcx + abx2 + -1abx2 + acx2 + -1acx2 + ax3 + -1ax3

Combine like terms: abcx + -1abcx = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = 0 + abx2 + -1abx2 + acx2 + -1acx2 + ax3 + -1ax3
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = abx2 + -1abx2 + acx2 + -1acx2 + ax3 + -1ax3

Combine like terms: abx2 + -1abx2 = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = 0 + acx2 + -1acx2 + ax3 + -1ax3
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = acx2 + -1acx2 + ax3 + -1ax3

Combine like terms: acx2 + -1acx2 = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = 0 + ax3 + -1ax3
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = ax3 + -1ax3

Combine like terms: ax3 + -1ax3 = 0
-1abcx + -1abx2 + -1acx2 + -1ax3 + -24x + -8x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1abc + -1abx + -1acx + -1ax2 + -24 + -8x + 2x2) = 0


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 '(-1abc + -1abx + -1acx + -1ax2 + -24 + -8x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1abc + -1abx + -1acx + -1ax2 + -24 + -8x + 2x2 = 0

Reorder the terms:
-24 + -1abc + -1abx + -1acx + -1ax2 + -8x + 2x2 = 0

Solving
-24 + -1abc + -1abx + -1acx + -1ax2 + -8x + 2x2 = 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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