6x^3-9x^2+12x=0

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Solution for 6x^3-9x^2+12x=0 equation: 


Simplifying
6x3 + -9x2 + 12x = 0

Reorder the terms:
12x + -9x2 + 6x3 = 0

Solving
12x + -9x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(4 + -3x + 2x2) = 0

Ignore the factor 3.

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 '(4 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x + 2x2 = 0

Solving
4 + -3x + 2x2 = 0

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

Divide each side by '2'.
2 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.5x + x2 = 0 + -2
-1.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.5x + x2 = -2

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -2 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -2 + 0.5625

Combine like terms: -2 + 0.5625 = -1.4375
0.5625 + -1.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -1.4375

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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