x^3+5x^2=4x-20x

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Solution for x^3+5x^2=4x-20x equation: 


Simplifying
x3 + 5x2 = 4x + -20x

Reorder the terms:
5x2 + x3 = 4x + -20x

Combine like terms: 4x + -20x = -16x
5x2 + x3 = -16x

Solving
5x2 + x3 = -16x

Solving for variable 'x'.

Reorder the terms:
16x + 5x2 + x3 = -16x + 16x

Combine like terms: -16x + 16x = 0
16x + 5x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + 5x + x2) = 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 '(16 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 5x + x2 = 0

Solving
16 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 5x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 5x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 5x + x2 = 0 + -16
5x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
5x + x2 = -16

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 = -16 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -16 + 6.25

Combine like terms: -16 + 6.25 = -9.75
6.25 + 5x + x2 = -9.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -9.75

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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