0=-2x^3+6x^2-6x

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Solution for 0=-2x^3+6x^2-6x equation: 


Simplifying
0 = -2x3 + 6x2 + -6x

Reorder the terms:
0 = -6x + 6x2 + -2x3

Solving
0 = -6x + 6x2 + -2x3

Solving for variable 'x'.
Remove the zero:
6x + -6x2 + 2x3 = -6x + 6x2 + -2x3 + 6x + -6x2 + 2x3

Reorder the terms:
6x + -6x2 + 2x3 = -6x + 6x + 6x2 + -6x2 + -2x3 + 2x3

Combine like terms: -6x + 6x = 0
6x + -6x2 + 2x3 = 0 + 6x2 + -6x2 + -2x3 + 2x3
6x + -6x2 + 2x3 = 6x2 + -6x2 + -2x3 + 2x3

Combine like terms: 6x2 + -6x2 = 0
6x + -6x2 + 2x3 = 0 + -2x3 + 2x3
6x + -6x2 + 2x3 = -2x3 + 2x3

Combine like terms: -2x3 + 2x3 = 0
6x + -6x2 + 2x3 = 0

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

Ignore the factor 2.

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 '(3 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -3x + x2 = 0

Solving
3 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -3x + x2 = 0 + -3

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

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -3 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + -3x + x2 = -0.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -0.75

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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