x(x^2+1)=x(2X^2-3)

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Solution for x(x^2+1)=x(2X^2-3) equation: 


Simplifying
x(x2 + 1) = x(2X2 + -3)

Reorder the terms:
x(1 + x2) = x(2X2 + -3)
(1 * x + x2 * x) = x(2X2 + -3)
(1x + x3) = x(2X2 + -3)

Reorder the terms:
1x + x3 = x(-3 + 2X2)
1x + x3 = (-3 * x + 2X2 * x)
1x + x3 = (-3x + 2xX2)

Solving
1x + x3 = -3x + 2xX2

Solving for variable 'x'.

Reorder the terms:
1x + 3x + -2xX2 + x3 = -3x + 2xX2 + 3x + -2xX2

Combine like terms: 1x + 3x = 4x
4x + -2xX2 + x3 = -3x + 2xX2 + 3x + -2xX2

Reorder the terms:
4x + -2xX2 + x3 = -3x + 3x + 2xX2 + -2xX2

Combine like terms: -3x + 3x = 0
4x + -2xX2 + x3 = 0 + 2xX2 + -2xX2
4x + -2xX2 + x3 = 2xX2 + -2xX2

Combine like terms: 2xX2 + -2xX2 = 0
4x + -2xX2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -2X2 + x2) = 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 '(4 + -2X2 + x2)' equal to zero and attempt to solve:

Simplifying
4 + -2X2 + x2 = 0

Solving
4 + -2X2 + x2 = 0

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

Add '-4' to each side of the equation.
4 + -2X2 + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -2X2 + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2X2 + x2 = 0 + -4
-2X2 + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2X2 + x2 = -4

Add '2X2' to each side of the equation.
-2X2 + 2X2 + x2 = -4 + 2X2

Combine like terms: -2X2 + 2X2 = 0
0 + x2 = -4 + 2X2
x2 = -4 + 2X2

Simplifying
x2 = -4 + 2X2

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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