0=5x^3+19x^2-4x

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Solution for 0=5x^3+19x^2-4x equation: 


Simplifying
0 = 5x3 + 19x2 + -4x

Reorder the terms:
0 = -4x + 19x2 + 5x3

Solving
0 = -4x + 19x2 + 5x3

Solving for variable 'x'.
Remove the zero:
4x + -19x2 + -5x3 = -4x + 19x2 + 5x3 + 4x + -19x2 + -5x3

Reorder the terms:
4x + -19x2 + -5x3 = -4x + 4x + 19x2 + -19x2 + 5x3 + -5x3

Combine like terms: -4x + 4x = 0
4x + -19x2 + -5x3 = 0 + 19x2 + -19x2 + 5x3 + -5x3
4x + -19x2 + -5x3 = 19x2 + -19x2 + 5x3 + -5x3

Combine like terms: 19x2 + -19x2 = 0
4x + -19x2 + -5x3 = 0 + 5x3 + -5x3
4x + -19x2 + -5x3 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
4x + -19x2 + -5x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -19x + -5x2) = 0

Factor a trinomial.
x((1 + -5x)(4 + x)) = 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 '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 3
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
Solution
x = {0, 0.2, -4}

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