2x^3=-3x^2+2x

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


Simplifying
2x3 = -3x2 + 2x

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

Solving
2x3 = 2x + -3x2

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -2, 0.5}

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