x=(x^3+10x^2+21x)(x^3-64)

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Solution for x=(x^3+10x^2+21x)(x^3-64) equation: 


Simplifying
x = (x3 + 10x2 + 21x)(x3 + -64)

Reorder the terms:
x = (21x + 10x2 + x3)(x3 + -64)

Reorder the terms:
x = (21x + 10x2 + x3)(-64 + x3)

Multiply (21x + 10x2 + x3) * (-64 + x3)
x = (21x * (-64 + x3) + 10x2 * (-64 + x3) + x3(-64 + x3))
x = ((-64 * 21x + x3 * 21x) + 10x2 * (-64 + x3) + x3(-64 + x3))
x = ((-1344x + 21x4) + 10x2 * (-64 + x3) + x3(-64 + x3))
x = (-1344x + 21x4 + (-64 * 10x2 + x3 * 10x2) + x3(-64 + x3))
x = (-1344x + 21x4 + (-640x2 + 10x5) + x3(-64 + x3))
x = (-1344x + 21x4 + -640x2 + 10x5 + (-64 * x3 + x3 * x3))
x = (-1344x + 21x4 + -640x2 + 10x5 + (-64x3 + x6))

Reorder the terms:
x = (-1344x + -640x2 + -64x3 + 21x4 + 10x5 + x6)
x = (-1344x + -640x2 + -64x3 + 21x4 + 10x5 + x6)

Solving
x = -1344x + -640x2 + -64x3 + 21x4 + 10x5 + x6

Solving for variable 'x'.

Combine like terms: x + 1344x = 1345x
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = -1344x + -640x2 + -64x3 + 21x4 + 10x5 + x6 + 1344x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6

Reorder the terms:
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = -1344x + 1344x + -640x2 + 640x2 + -64x3 + 64x3 + 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6

Combine like terms: -1344x + 1344x = 0
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 0 + -640x2 + 640x2 + -64x3 + 64x3 + 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = -640x2 + 640x2 + -64x3 + 64x3 + 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6

Combine like terms: -640x2 + 640x2 = 0
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 0 + -64x3 + 64x3 + 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = -64x3 + 64x3 + 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6

Combine like terms: -64x3 + 64x3 = 0
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 0 + 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 21x4 + -21x4 + 10x5 + -10x5 + x6 + -1x6

Combine like terms: 21x4 + -21x4 = 0
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 0 + 10x5 + -10x5 + x6 + -1x6
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 10x5 + -10x5 + x6 + -1x6

Combine like terms: 10x5 + -10x5 = 0
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 0 + x6 + -1x6
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = x6 + -1x6

Combine like terms: x6 + -1x6 = 0
1345x + 640x2 + 64x3 + -21x4 + -10x5 + -1x6 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1345 + 640x + 64x2 + -21x3 + -10x4 + -1x5) = 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 '(1345 + 640x + 64x2 + -21x3 + -10x4 + -1x5)' equal to zero and attempt to solve:

Simplifying
1345 + 640x + 64x2 + -21x3 + -10x4 + -1x5 = 0

Solving
1345 + 640x + 64x2 + -21x3 + -10x4 + -1x5 = 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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