2x(x^2+x)+4x=0

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Solution for 2x(x^2+x)+4x=0 equation: 


Simplifying
2x(x2 + x) + 4x = 0

Reorder the terms:
2x(x + x2) + 4x = 0
(x * 2x + x2 * 2x) + 4x = 0
(2x2 + 2x3) + 4x = 0

Reorder the terms:
4x + 2x2 + 2x3 = 0

Solving
4x + 2x2 + 2x3 = 0

Solving for variable 'x'.

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

Simplifying
2 + x + x2 = 0

Solving
2 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

Reorder the terms:
2 + -2 + x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x + x2 = 0 + -2
x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
x + x2 = -2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -2 + 0.25

Reorder the terms:
0.25 + x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + x + x2 = -1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.75

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}

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