(x^2+4x)(x^2+x-6)=(x^3-9x)(x^2+2x-8)

Solution for (x^2+4x)(x^2+x-6)=(x^3-9x)(x^2+2x-8) equation:

Simplifying
(x2 + 4x)(x2 + x + -6) = (x3 + -9x)(x2 + 2x + -8)

Reorder the terms:
(4x + x2)(x2 + x + -6) = (x3 + -9x)(x2 + 2x + -8)

Reorder the terms:
(4x + x2)(-6 + x + x2) = (x3 + -9x)(x2 + 2x + -8)

Multiply (4x + x2) * (-6 + x + x2)
(4x * (-6 + x + x2) + x2(-6 + x + x2)) = (x3 + -9x)(x2 + 2x + -8)
((-6 * 4x + x * 4x + x2 * 4x) + x2(-6 + x + x2)) = (x3 + -9x)(x2 + 2x + -8)
((-24x + 4x2 + 4x3) + x2(-6 + x + x2)) = (x3 + -9x)(x2 + 2x + -8)
(-24x + 4x2 + 4x3 + (-6 * x2 + x * x2 + x2 * x2)) = (x3 + -9x)(x2 + 2x + -8)
(-24x + 4x2 + 4x3 + (-6x2 + x3 + x4)) = (x3 + -9x)(x2 + 2x + -8)

Reorder the terms:
(-24x + 4x2 + -6x2 + 4x3 + x3 + x4) = (x3 + -9x)(x2 + 2x + -8)

Combine like terms: 4x2 + -6x2 = -2x2
(-24x + -2x2 + 4x3 + x3 + x4) = (x3 + -9x)(x2 + 2x + -8)

Combine like terms: 4x3 + x3 = 5x3
(-24x + -2x2 + 5x3 + x4) = (x3 + -9x)(x2 + 2x + -8)

Reorder the terms:
-24x + -2x2 + 5x3 + x4 = (-9x + x3)(x2 + 2x + -8)

Reorder the terms:
-24x + -2x2 + 5x3 + x4 = (-9x + x3)(-8 + 2x + x2)

Multiply (-9x + x3) * (-8 + 2x + x2)
-24x + -2x2 + 5x3 + x4 = (-9x * (-8 + 2x + x2) + x3(-8 + 2x + x2))
-24x + -2x2 + 5x3 + x4 = ((-8 * -9x + 2x * -9x + x2 * -9x) + x3(-8 + 2x + x2))
-24x + -2x2 + 5x3 + x4 = ((72x + -18x2 + -9x3) + x3(-8 + 2x + x2))
-24x + -2x2 + 5x3 + x4 = (72x + -18x2 + -9x3 + (-8 * x3 + 2x * x3 + x2 * x3))
-24x + -2x2 + 5x3 + x4 = (72x + -18x2 + -9x3 + (-8x3 + 2x4 + x5))

Combine like terms: -9x3 + -8x3 = -17x3
-24x + -2x2 + 5x3 + x4 = (72x + -18x2 + -17x3 + 2x4 + x5)

Solving
-24x + -2x2 + 5x3 + x4 = 72x + -18x2 + -17x3 + 2x4 + x5

Solving for variable 'x'.

Reorder the terms:
-24x + -72x + -2x2 + 18x2 + 5x3 + 17x3 + x4 + -2x4 + -1x5 = 72x + -18x2 + -17x3 + 2x4 + x5 + -72x + 18x2 + 17x3 + -2x4 + -1x5

Combine like terms: -24x + -72x = -96x
-96x + -2x2 + 18x2 + 5x3 + 17x3 + x4 + -2x4 + -1x5 = 72x + -18x2 + -17x3 + 2x4 + x5 + -72x + 18x2 + 17x3 + -2x4 + -1x5

Combine like terms: -2x2 + 18x2 = 16x2
-96x + 16x2 + 5x3 + 17x3 + x4 + -2x4 + -1x5 = 72x + -18x2 + -17x3 + 2x4 + x5 + -72x + 18x2 + 17x3 + -2x4 + -1x5

Combine like terms: 5x3 + 17x3 = 22x3
-96x + 16x2 + 22x3 + x4 + -2x4 + -1x5 = 72x + -18x2 + -17x3 + 2x4 + x5 + -72x + 18x2 + 17x3 + -2x4 + -1x5

Combine like terms: x4 + -2x4 = -1x4
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 72x + -18x2 + -17x3 + 2x4 + x5 + -72x + 18x2 + 17x3 + -2x4 + -1x5

Reorder the terms:
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 72x + -72x + -18x2 + 18x2 + -17x3 + 17x3 + 2x4 + -2x4 + x5 + -1x5

Combine like terms: 72x + -72x = 0
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 0 + -18x2 + 18x2 + -17x3 + 17x3 + 2x4 + -2x4 + x5 + -1x5
-96x + 16x2 + 22x3 + -1x4 + -1x5 = -18x2 + 18x2 + -17x3 + 17x3 + 2x4 + -2x4 + x5 + -1x5

Combine like terms: -18x2 + 18x2 = 0
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 0 + -17x3 + 17x3 + 2x4 + -2x4 + x5 + -1x5
-96x + 16x2 + 22x3 + -1x4 + -1x5 = -17x3 + 17x3 + 2x4 + -2x4 + x5 + -1x5

Combine like terms: -17x3 + 17x3 = 0
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 0 + 2x4 + -2x4 + x5 + -1x5
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 2x4 + -2x4 + x5 + -1x5

Combine like terms: 2x4 + -2x4 = 0
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 0 + x5 + -1x5
-96x + 16x2 + 22x3 + -1x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-96x + 16x2 + 22x3 + -1x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-96 + 16x + 22x2 + -1x3 + -1x4) = 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 '(-96 + 16x + 22x2 + -1x3 + -1x4)' equal to zero and attempt to solve:

Simplifying
-96 + 16x + 22x2 + -1x3 + -1x4 = 0

Solving
-96 + 16x + 22x2 + -1x3 + -1x4 = 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}