0=x^3+5x^2+4x

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Solution for 0=x^3+5x^2+4x equation: 


Simplifying
0 = x3 + 5x2 + 4x

Reorder the terms:
0 = 4x + 5x2 + x3

Solving
0 = 4x + 5x2 + x3

Solving for variable 'x'.
Remove the zero:
-4x + -5x2 + -1x3 = 4x + 5x2 + x3 + -4x + -5x2 + -1x3

Reorder the terms:
-4x + -5x2 + -1x3 = 4x + -4x + 5x2 + -5x2 + x3 + -1x3

Combine like terms: 4x + -4x = 0
-4x + -5x2 + -1x3 = 0 + 5x2 + -5x2 + x3 + -1x3
-4x + -5x2 + -1x3 = 5x2 + -5x2 + x3 + -1x3

Combine like terms: 5x2 + -5x2 = 0
-4x + -5x2 + -1x3 = 0 + x3 + -1x3
-4x + -5x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-4x + -5x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(4 + 5x + x2) = 0

Factor a trinomial.
-1x((4 + x)(1 + x)) = 0

Ignore the factor -1.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {0, -4, -1}

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