0=x(5x-2)(x^2+1)

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Solution for 0=x(5x-2)(x^2+1) equation: 


Simplifying
0 = x(5x + -2)(x2 + 1)

Reorder the terms:
0 = x(-2 + 5x)(x2 + 1)

Reorder the terms:
0 = x(-2 + 5x)(1 + x2)

Multiply (-2 + 5x) * (1 + x2)
0 = x(-2(1 + x2) + 5x * (1 + x2))
0 = x((1 * -2 + x2 * -2) + 5x * (1 + x2))
0 = x((-2 + -2x2) + 5x * (1 + x2))
0 = x(-2 + -2x2 + (1 * 5x + x2 * 5x))
0 = x(-2 + -2x2 + (5x + 5x3))

Reorder the terms:
0 = x(-2 + 5x + -2x2 + 5x3)
0 = x(-2 + 5x + -2x2 + 5x3)
0 = (-2 * x + 5x * x + -2x2 * x + 5x3 * x)
0 = (-2x + 5x2 + -2x3 + 5x4)

Solving
0 = -2x + 5x2 + -2x3 + 5x4

Solving for variable 'x'.
Remove the zero:
2x + -5x2 + 2x3 + -5x4 = -2x + 5x2 + -2x3 + 5x4 + 2x + -5x2 + 2x3 + -5x4

Reorder the terms:
2x + -5x2 + 2x3 + -5x4 = -2x + 2x + 5x2 + -5x2 + -2x3 + 2x3 + 5x4 + -5x4

Combine like terms: -2x + 2x = 0
2x + -5x2 + 2x3 + -5x4 = 0 + 5x2 + -5x2 + -2x3 + 2x3 + 5x4 + -5x4
2x + -5x2 + 2x3 + -5x4 = 5x2 + -5x2 + -2x3 + 2x3 + 5x4 + -5x4

Combine like terms: 5x2 + -5x2 = 0
2x + -5x2 + 2x3 + -5x4 = 0 + -2x3 + 2x3 + 5x4 + -5x4
2x + -5x2 + 2x3 + -5x4 = -2x3 + 2x3 + 5x4 + -5x4

Combine like terms: -2x3 + 2x3 = 0
2x + -5x2 + 2x3 + -5x4 = 0 + 5x4 + -5x4
2x + -5x2 + 2x3 + -5x4 = 5x4 + -5x4

Combine like terms: 5x4 + -5x4 = 0
2x + -5x2 + 2x3 + -5x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + -5x + 2x2 + -5x3) = 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 '(2 + -5x + 2x2 + -5x3)' equal to zero and attempt to solve:

Simplifying
2 + -5x + 2x2 + -5x3 = 0

Solving
2 + -5x + 2x2 + -5x3 = 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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