4x^3+20x^2+153x=0

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Solution for 4x^3+20x^2+153x=0 equation: 


Simplifying
4x3 + 20x2 + 153x = 0

Reorder the terms:
153x + 20x2 + 4x3 = 0

Solving
153x + 20x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(153 + 20x + 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 '(153 + 20x + 4x2)' equal to zero and attempt to solve:

Simplifying
153 + 20x + 4x2 = 0

Solving
153 + 20x + 4x2 = 0

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

Divide each side by '4'.
38.25 + 5x + x2 = 0

Move the constant term to the right:

Add '-38.25' to each side of the equation.
38.25 + 5x + -38.25 + x2 = 0 + -38.25

Reorder the terms:
38.25 + -38.25 + 5x + x2 = 0 + -38.25

Combine like terms: 38.25 + -38.25 = 0.00
0.00 + 5x + x2 = 0 + -38.25
5x + x2 = 0 + -38.25

Combine like terms: 0 + -38.25 = -38.25
5x + x2 = -38.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -38.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -38.25 + 6.25

Combine like terms: -38.25 + 6.25 = -32
6.25 + 5x + x2 = -32

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -32

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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