4*x^3+12*x^2+123*x=0

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Solution for 4*x^3+12*x^2+123*x=0 equation: 


Simplifying
4x3 + 12x2 + 123x = 0

Reorder the terms:
123x + 12x2 + 4x3 = 0

Solving
123x + 12x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(123 + 12x + 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 '(123 + 12x + 4x2)' equal to zero and attempt to solve:

Simplifying
123 + 12x + 4x2 = 0

Solving
123 + 12x + 4x2 = 0

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

Divide each side by '4'.
30.75 + 3x + x2 = 0

Move the constant term to the right:

Add '-30.75' to each side of the equation.
30.75 + 3x + -30.75 + x2 = 0 + -30.75

Reorder the terms:
30.75 + -30.75 + 3x + x2 = 0 + -30.75

Combine like terms: 30.75 + -30.75 = 0.00
0.00 + 3x + x2 = 0 + -30.75
3x + x2 = 0 + -30.75

Combine like terms: 0 + -30.75 = -30.75
3x + x2 = -30.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -30.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -30.75 + 2.25

Combine like terms: -30.75 + 2.25 = -28.5
2.25 + 3x + x2 = -28.5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -28.5

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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