4x^3+4x^2+15x=0

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Solution for 4x^3+4x^2+15x=0 equation: 


Simplifying
4x3 + 4x2 + 15x = 0

Reorder the terms:
15x + 4x2 + 4x3 = 0

Solving
15x + 4x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + 4x + 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 '(15 + 4x + 4x2)' equal to zero and attempt to solve:

Simplifying
15 + 4x + 4x2 = 0

Solving
15 + 4x + 4x2 = 0

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

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

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x + x2 = 0 + -3.75
x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
x + x2 = -3.75

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.
 + 0.25 + x2 = -3.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -3.75 + 0.25

Combine like terms: -3.75 + 0.25 = -3.5
1.25 + x2 = -3.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.5

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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