9x^4-6x^3+4x^2=0

Solution for 9x^4-6x^3+4x^2=0 equation:

Simplifying
9x4 + -6x3 + 4x2 = 0

Reorder the terms:
4x2 + -6x3 + 9x4 = 0

Solving
4x2 + -6x3 + 9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + -6x + 9x2) = 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 '(4 + -6x + 9x2)' equal to zero and attempt to solve:

Simplifying
4 + -6x + 9x2 = 0

Solving
4 + -6x + 9x2 = 0

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

Divide each side by '9'.
0.4444444444 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -0.6666666667x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -0.6666666667x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + -0.4444444444
-0.6666666667x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-0.6666666667x + x2 = -0.4444444444

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -0.4444444444 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -0.4444444444 + 0.1111111112

Combine like terms: -0.4444444444 + 0.1111111112 = -0.3333333332
0.1111111112 + -0.6666666667x + x2 = -0.3333333332

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -0.3333333332

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}