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

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


Simplifying
0 = 5x3 + 3x2 + -2x

Reorder the terms:
0 = -2x + 3x2 + 5x3

Solving
0 = -2x + 3x2 + 5x3

Solving for variable 'x'.
Remove the zero:
2x + -3x2 + -5x3 = -2x + 3x2 + 5x3 + 2x + -3x2 + -5x3

Reorder the terms:
2x + -3x2 + -5x3 = -2x + 2x + 3x2 + -3x2 + 5x3 + -5x3

Combine like terms: -2x + 2x = 0
2x + -3x2 + -5x3 = 0 + 3x2 + -3x2 + 5x3 + -5x3
2x + -3x2 + -5x3 = 3x2 + -3x2 + 5x3 + -5x3

Combine like terms: 3x2 + -3x2 = 0
2x + -3x2 + -5x3 = 0 + 5x3 + -5x3
2x + -3x2 + -5x3 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
2x + -3x2 + -5x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + -3x + -5x2) = 0

Factor a trinomial.
x((2 + -5x)(1 + 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 '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

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, 0.4, -1}

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