(2x-1)(2x^3-50x)=0

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Solution for (2x-1)(2x^3-50x)=0 equation: 


Simplifying
(2x + -1)(2x3 + -50x) = 0

Reorder the terms:
(-1 + 2x)(2x3 + -50x) = 0

Reorder the terms:
(-1 + 2x)(-50x + 2x3) = 0

Multiply (-1 + 2x) * (-50x + 2x3)
(-1(-50x + 2x3) + 2x * (-50x + 2x3)) = 0
((-50x * -1 + 2x3 * -1) + 2x * (-50x + 2x3)) = 0
((50x + -2x3) + 2x * (-50x + 2x3)) = 0
(50x + -2x3 + (-50x * 2x + 2x3 * 2x)) = 0
(50x + -2x3 + (-100x2 + 4x4)) = 0

Reorder the terms:
(50x + -100x2 + -2x3 + 4x4) = 0
(50x + -100x2 + -2x3 + 4x4) = 0

Solving
50x + -100x2 + -2x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(25 + -50x + -1x2 + 2x3) = 0

Ignore the factor 2.

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 '(25 + -50x + -1x2 + 2x3)' equal to zero and attempt to solve:

Simplifying
25 + -50x + -1x2 + 2x3 = 0

Solving
25 + -50x + -1x2 + 2x3 = 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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