x^3+x=3x^2-3x^3

Solution for x^3+x=3x^2-3x^3 equation:

Simplifying
x3 + x = 3x2 + -3x3

Reorder the terms:
x + x3 = 3x2 + -3x3

Solving
x + x3 = 3x2 + -3x3

Solving for variable 'x'.

Reorder the terms:
x + -3x2 + x3 + 3x3 = 3x2 + -3x3 + -3x2 + 3x3

Combine like terms: x3 + 3x3 = 4x3
x + -3x2 + 4x3 = 3x2 + -3x3 + -3x2 + 3x3

Reorder the terms:
x + -3x2 + 4x3 = 3x2 + -3x2 + -3x3 + 3x3

Combine like terms: 3x2 + -3x2 = 0
x + -3x2 + 4x3 = 0 + -3x3 + 3x3
x + -3x2 + 4x3 = -3x3 + 3x3

Combine like terms: -3x3 + 3x3 = 0
x + -3x2 + 4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -3x + 4x2) = 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 '(1 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + -3x + 4x2 = 0

Solving
1 + -3x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.75x + x2 = 0 + -0.25
-0.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.75x + x2 = -0.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + -0.75x + x2 = -0.109375

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = -0.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}