(24x^2-6x^5)(4-4x^3+x^5)-(8x^3-x^6)(-8x+4x^4)=0

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Solution for (24x^2-6x^5)(4-4x^3+x^5)-(8x^3-x^6)(-8x+4x^4)=0 equation: 


Simplifying
(24x2 + -6x5)(4 + -4x3 + x5) + -1(8x3 + -1x6)(-8x + 4x4) = 0

Multiply (24x2 + -6x5) * (4 + -4x3 + x5)
(24x2 * (4 + -4x3 + x5) + -6x5 * (4 + -4x3 + x5)) + -1(8x3 + -1x6)(-8x + 4x4) = 0
((4 * 24x2 + -4x3 * 24x2 + x5 * 24x2) + -6x5 * (4 + -4x3 + x5)) + -1(8x3 + -1x6)(-8x + 4x4) = 0
((96x2 + -96x5 + 24x7) + -6x5 * (4 + -4x3 + x5)) + -1(8x3 + -1x6)(-8x + 4x4) = 0
(96x2 + -96x5 + 24x7 + (4 * -6x5 + -4x3 * -6x5 + x5 * -6x5)) + -1(8x3 + -1x6)(-8x + 4x4) = 0
(96x2 + -96x5 + 24x7 + (-24x5 + 24x8 + -6x10)) + -1(8x3 + -1x6)(-8x + 4x4) = 0

Reorder the terms:
(96x2 + -96x5 + -24x5 + 24x7 + 24x8 + -6x10) + -1(8x3 + -1x6)(-8x + 4x4) = 0

Combine like terms: -96x5 + -24x5 = -120x5
(96x2 + -120x5 + 24x7 + 24x8 + -6x10) + -1(8x3 + -1x6)(-8x + 4x4) = 0

Multiply (8x3 + -1x6) * (-8x + 4x4)
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + -1(8x3 * (-8x + 4x4) + -1x6 * (-8x + 4x4)) = 0
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + -1((-8x * 8x3 + 4x4 * 8x3) + -1x6 * (-8x + 4x4)) = 0
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + -1((-64x4 + 32x7) + -1x6 * (-8x + 4x4)) = 0
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + -1(-64x4 + 32x7 + (-8x * -1x6 + 4x4 * -1x6)) = 0
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + -1(-64x4 + 32x7 + (8x7 + -4x10)) = 0

Combine like terms: 32x7 + 8x7 = 40x7
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + -1(-64x4 + 40x7 + -4x10) = 0
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + (-64x4 * -1 + 40x7 * -1 + -4x10 * -1) = 0
96x2 + -120x5 + 24x7 + 24x8 + -6x10 + (64x4 + -40x7 + 4x10) = 0

Reorder the terms:
96x2 + 64x4 + -120x5 + 24x7 + -40x7 + 24x8 + -6x10 + 4x10 = 0

Combine like terms: 24x7 + -40x7 = -16x7
96x2 + 64x4 + -120x5 + -16x7 + 24x8 + -6x10 + 4x10 = 0

Combine like terms: -6x10 + 4x10 = -2x10
96x2 + 64x4 + -120x5 + -16x7 + 24x8 + -2x10 = 0

Solving
96x2 + 64x4 + -120x5 + -16x7 + 24x8 + -2x10 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(48 + 32x2 + -60x3 + -8x5 + 12x6 + -1x8) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(48 + 32x2 + -60x3 + -8x5 + 12x6 + -1x8)' equal to zero and attempt to solve:

Simplifying
48 + 32x2 + -60x3 + -8x5 + 12x6 + -1x8 = 0

Solving
48 + 32x2 + -60x3 + -8x5 + 12x6 + -1x8 = 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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