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

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


Simplifying
6x4 + -3x3 + 2x2 = 0

Reorder the terms:
2x2 + -3x3 + 6x4 = 0

Solving
2x2 + -3x3 + 6x4 = 0

Solving for variable 'x'.

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


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 '(2 + -3x + 6x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x + 6x2 = 0

Solving
2 + -3x + 6x2 = 0

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

Divide each side by '6'.
0.3333333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -0.5x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -0.5x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + -0.3333333333
-0.5x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-0.5x + x2 = -0.3333333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.3333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.3333333333 + 0.0625

Combine like terms: -0.3333333333 + 0.0625 = -0.2708333333
0.0625 + -0.5x + x2 = -0.2708333333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.2708333333

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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