x^3=6x^2-12x

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Solution for x^3=6x^2-12x equation: 


Simplifying
x3 = 6x2 + -12x

Reorder the terms:
x3 = -12x + 6x2

Solving
x3 = -12x + 6x2

Solving for variable 'x'.

Reorder the terms:
12x + -6x2 + x3 = -12x + 6x2 + 12x + -6x2

Reorder the terms:
12x + -6x2 + x3 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
12x + -6x2 + x3 = 0 + 6x2 + -6x2
12x + -6x2 + x3 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
12x + -6x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + -6x + x2) = 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 '(12 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
12 + -6x + x2 = 0

Solving
12 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -6x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -6x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -6x + x2 = 0 + -12
-6x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-6x + x2 = -12

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -12 + 9

Reorder the terms:
9 + -6x + x2 = -12 + 9

Combine like terms: -12 + 9 = -3
9 + -6x + x2 = -3

Factor a perfect square on the left side:
(x + -3)(x + -3) = -3

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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