(x^2+5x)(x^2-3x-28)=(x^3-16x)(x^2-2x-35)

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Solution for (x^2+5x)(x^2-3x-28)=(x^3-16x)(x^2-2x-35) equation: 


Simplifying
(x2 + 5x)(x2 + -3x + -28) = (x3 + -16x)(x2 + -2x + -35)

Reorder the terms:
(5x + x2)(x2 + -3x + -28) = (x3 + -16x)(x2 + -2x + -35)

Reorder the terms:
(5x + x2)(-28 + -3x + x2) = (x3 + -16x)(x2 + -2x + -35)

Multiply (5x + x2) * (-28 + -3x + x2)
(5x * (-28 + -3x + x2) + x2(-28 + -3x + x2)) = (x3 + -16x)(x2 + -2x + -35)
((-28 * 5x + -3x * 5x + x2 * 5x) + x2(-28 + -3x + x2)) = (x3 + -16x)(x2 + -2x + -35)
((-140x + -15x2 + 5x3) + x2(-28 + -3x + x2)) = (x3 + -16x)(x2 + -2x + -35)
(-140x + -15x2 + 5x3 + (-28 * x2 + -3x * x2 + x2 * x2)) = (x3 + -16x)(x2 + -2x + -35)
(-140x + -15x2 + 5x3 + (-28x2 + -3x3 + x4)) = (x3 + -16x)(x2 + -2x + -35)

Reorder the terms:
(-140x + -15x2 + -28x2 + 5x3 + -3x3 + x4) = (x3 + -16x)(x2 + -2x + -35)

Combine like terms: -15x2 + -28x2 = -43x2
(-140x + -43x2 + 5x3 + -3x3 + x4) = (x3 + -16x)(x2 + -2x + -35)

Combine like terms: 5x3 + -3x3 = 2x3
(-140x + -43x2 + 2x3 + x4) = (x3 + -16x)(x2 + -2x + -35)

Reorder the terms:
-140x + -43x2 + 2x3 + x4 = (-16x + x3)(x2 + -2x + -35)

Reorder the terms:
-140x + -43x2 + 2x3 + x4 = (-16x + x3)(-35 + -2x + x2)

Multiply (-16x + x3) * (-35 + -2x + x2)
-140x + -43x2 + 2x3 + x4 = (-16x * (-35 + -2x + x2) + x3(-35 + -2x + x2))
-140x + -43x2 + 2x3 + x4 = ((-35 * -16x + -2x * -16x + x2 * -16x) + x3(-35 + -2x + x2))
-140x + -43x2 + 2x3 + x4 = ((560x + 32x2 + -16x3) + x3(-35 + -2x + x2))
-140x + -43x2 + 2x3 + x4 = (560x + 32x2 + -16x3 + (-35 * x3 + -2x * x3 + x2 * x3))
-140x + -43x2 + 2x3 + x4 = (560x + 32x2 + -16x3 + (-35x3 + -2x4 + x5))

Combine like terms: -16x3 + -35x3 = -51x3
-140x + -43x2 + 2x3 + x4 = (560x + 32x2 + -51x3 + -2x4 + x5)

Solving
-140x + -43x2 + 2x3 + x4 = 560x + 32x2 + -51x3 + -2x4 + x5

Solving for variable 'x'.

Reorder the terms:
-140x + -560x + -43x2 + -32x2 + 2x3 + 51x3 + x4 + 2x4 + -1x5 = 560x + 32x2 + -51x3 + -2x4 + x5 + -560x + -32x2 + 51x3 + 2x4 + -1x5

Combine like terms: -140x + -560x = -700x
-700x + -43x2 + -32x2 + 2x3 + 51x3 + x4 + 2x4 + -1x5 = 560x + 32x2 + -51x3 + -2x4 + x5 + -560x + -32x2 + 51x3 + 2x4 + -1x5

Combine like terms: -43x2 + -32x2 = -75x2
-700x + -75x2 + 2x3 + 51x3 + x4 + 2x4 + -1x5 = 560x + 32x2 + -51x3 + -2x4 + x5 + -560x + -32x2 + 51x3 + 2x4 + -1x5

Combine like terms: 2x3 + 51x3 = 53x3
-700x + -75x2 + 53x3 + x4 + 2x4 + -1x5 = 560x + 32x2 + -51x3 + -2x4 + x5 + -560x + -32x2 + 51x3 + 2x4 + -1x5

Combine like terms: x4 + 2x4 = 3x4
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 560x + 32x2 + -51x3 + -2x4 + x5 + -560x + -32x2 + 51x3 + 2x4 + -1x5

Reorder the terms:
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 560x + -560x + 32x2 + -32x2 + -51x3 + 51x3 + -2x4 + 2x4 + x5 + -1x5

Combine like terms: 560x + -560x = 0
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 0 + 32x2 + -32x2 + -51x3 + 51x3 + -2x4 + 2x4 + x5 + -1x5
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 32x2 + -32x2 + -51x3 + 51x3 + -2x4 + 2x4 + x5 + -1x5

Combine like terms: 32x2 + -32x2 = 0
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 0 + -51x3 + 51x3 + -2x4 + 2x4 + x5 + -1x5
-700x + -75x2 + 53x3 + 3x4 + -1x5 = -51x3 + 51x3 + -2x4 + 2x4 + x5 + -1x5

Combine like terms: -51x3 + 51x3 = 0
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 0 + -2x4 + 2x4 + x5 + -1x5
-700x + -75x2 + 53x3 + 3x4 + -1x5 = -2x4 + 2x4 + x5 + -1x5

Combine like terms: -2x4 + 2x4 = 0
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 0 + x5 + -1x5
-700x + -75x2 + 53x3 + 3x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-700x + -75x2 + 53x3 + 3x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-700 + -75x + 53x2 + 3x3 + -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 '(-700 + -75x + 53x2 + 3x3 + -1x4)' equal to zero and attempt to solve:

Simplifying
-700 + -75x + 53x2 + 3x3 + -1x4 = 0

Solving
-700 + -75x + 53x2 + 3x3 + -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}

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