4y^4-8y^3+6y^2=0

Solution for 4y^4-8y^3+6y^2=0 equation:

Simplifying
4y4 + -8y3 + 6y2 = 0

Reorder the terms:
6y2 + -8y3 + 4y4 = 0

Solving
6y2 + -8y3 + 4y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(3 + -4y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(3 + -4y + 2y2)' equal to zero and attempt to solve:

Simplifying
3 + -4y + 2y2 = 0

Solving
3 + -4y + 2y2 = 0

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

Divide each side by '2'.
1.5 + -2y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -2y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -2y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -2y + y2 = 0 + -1.5
-2y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-2y + y2 = -1.5

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = -1.5 + 1

Reorder the terms:
1 + -2y + y2 = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
1 + -2y + y2 = -0.5

Factor a perfect square on the left side:
(y + -1)(y + -1) = -0.5

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
y = {0}