0=4x^5+16x^4+20x^33+16x^2+16x

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Solution for 0=4x^5+16x^4+20x^33+16x^2+16x equation:


Simplifying
0 = 4x5 + 16x4 + 20x33 + 16x2 + 16x

Reorder the terms:
0 = 16x + 16x2 + 16x4 + 4x5 + 20x33

Solving
0 = 16x + 16x2 + 16x4 + 4x5 + 20x33

Solving for variable 'x'.
Remove the zero:
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 16x + 16x2 + 16x4 + 4x5 + 20x33 + -16x + -16x2 + -16x4 + -4x5 + -20x33

Reorder the terms:
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 16x + -16x + 16x2 + -16x2 + 16x4 + -16x4 + 4x5 + -4x5 + 20x33 + -20x33

Combine like terms: 16x + -16x = 0
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 0 + 16x2 + -16x2 + 16x4 + -16x4 + 4x5 + -4x5 + 20x33 + -20x33
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 16x2 + -16x2 + 16x4 + -16x4 + 4x5 + -4x5 + 20x33 + -20x33

Combine like terms: 16x2 + -16x2 = 0
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 0 + 16x4 + -16x4 + 4x5 + -4x5 + 20x33 + -20x33
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 16x4 + -16x4 + 4x5 + -4x5 + 20x33 + -20x33

Combine like terms: 16x4 + -16x4 = 0
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 0 + 4x5 + -4x5 + 20x33 + -20x33
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 4x5 + -4x5 + 20x33 + -20x33

Combine like terms: 4x5 + -4x5 = 0
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 0 + 20x33 + -20x33
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 20x33 + -20x33

Combine like terms: 20x33 + -20x33 = 0
-16x + -16x2 + -16x4 + -4x5 + -20x33 = 0

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(4 + 4x + 4x3 + x4 + 5x32) = 0

Ignore the factor -4.

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 '(4 + 4x + 4x3 + x4 + 5x32)' equal to zero and attempt to solve: Simplifying 4 + 4x + 4x3 + x4 + 5x32 = 0 Solving 4 + 4x + 4x3 + x4 + 5x32 = 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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