12x^3-32x^2+48x=0

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Solution for 12x^3-32x^2+48x=0 equation: 


Simplifying
12x3 + -32x2 + 48x = 0

Reorder the terms:
48x + -32x2 + 12x3 = 0

Solving
48x + -32x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(12 + -8x + 3x2) = 0

Ignore the factor 4.

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 + -8x + 3x2)' equal to zero and attempt to solve:

Simplifying
12 + -8x + 3x2 = 0

Solving
12 + -8x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
4 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2.666666667x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -2.666666667x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2.666666667x + x2 = 0 + -4
-2.666666667x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2.666666667x + x2 = -4

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -4 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -4 + 1.777777780

Combine like terms: -4 + 1.777777780 = -2.22222222
1.777777780 + -2.666666667x + x2 = -2.22222222

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = -2.22222222

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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