24x^3+8x^2+4x=0

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Solution for 24x^3+8x^2+4x=0 equation: 


Simplifying
24x3 + 8x2 + 4x = 0

Reorder the terms:
4x + 8x2 + 24x3 = 0

Solving
4x + 8x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + 2x + 6x2) = 0

Ignore the factor 4.

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 + 2x + 6x2)' equal to zero and attempt to solve:

Simplifying
1 + 2x + 6x2 = 0

Solving
1 + 2x + 6x2 = 0

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

Divide each side by '6'.
0.1666666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 0.3333333333x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 0.3333333333x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + -0.1666666667
0.3333333333x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
0.3333333333x + x2 = -0.1666666667

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = -0.1666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = -0.1666666667 + 0.02777777779

Combine like terms: -0.1666666667 + 0.02777777779 = -0.13888888891
0.02777777779 + 0.3333333333x + x2 = -0.13888888891

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = -0.13888888891

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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