3x^3+5x^2+28x=0

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Solution for 3x^3+5x^2+28x=0 equation: 


Simplifying
3x3 + 5x2 + 28x = 0

Reorder the terms:
28x + 5x2 + 3x3 = 0

Solving
28x + 5x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(28 + 5x + 3x2) = 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 '(28 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
28 + 5x + 3x2 = 0

Solving
28 + 5x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + 1.666666667x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + 1.666666667x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + -9.333333333
1.666666667x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
1.666666667x + x2 = -9.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -9.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -9.333333333 + 0.6944444447

Combine like terms: -9.333333333 + 0.6944444447 = -8.6388888883
0.6944444447 + 1.666666667x + x2 = -8.6388888883

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -8.6388888883

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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