-18x^4+6x^3-3x^2=0

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Solution for -18x^4+6x^3-3x^2=0 equation: 


Simplifying
-18x4 + 6x3 + -3x2 = 0

Reorder the terms:
-3x2 + 6x3 + -18x4 = 0

Solving
-3x2 + 6x3 + -18x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-1 + 2x + -6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-1 + 2x + -6x2)' equal to zero and attempt to solve:

Simplifying
-1 + 2x + -6x2 = 0

Solving
-1 + 2x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.1666666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.3333333333x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -0.3333333333x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -0.3333333333x + x2 = 0 + -0.1666666667
-0.3333333333x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-0.3333333333x + x2 = -0.1666666667

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = -0.1666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = -0.1666666667 + 0.02777777779

Combine like terms: -0.1666666667 + 0.02777777779 = -0.13888888891
0.02777777779 + -0.3333333333x + x2 = -0.13888888891

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = -0.13888888891

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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