9y^2(6y^2-4y+6)=

Solution for 9y^2(6y^2-4y+6)= equation:

Simplifying
9y2(6y2 + -4y + 6) = 0

Reorder the terms:
9y2(6 + -4y + 6y2) = 0
(6 * 9y2 + -4y * 9y2 + 6y2 * 9y2) = 0
(54y2 + -36y3 + 54y4) = 0

Solving
54y2 + -36y3 + 54y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '18y2'.
18y2(3 + -2y + 3y2) = 0

Ignore the factor 18.
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 + -2y + 3y2)' equal to zero and attempt to solve:

Simplifying
3 + -2y + 3y2 = 0

Solving
3 + -2y + 3y2 = 0

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

Divide each side by '3'.
1 + -0.6666666667y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.6666666667y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -0.6666666667y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.6666666667y + y2 = 0 + -1
-0.6666666667y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.6666666667y + y2 = -1

The y term is -0.6666666667y.  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.
-0.6666666667y + 0.1111111112 + y2 = -1 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667y + y2 = -1 + 0.1111111112

Combine like terms: -1 + 0.1111111112 = -0.8888888888
0.1111111112 + -0.6666666667y + y2 = -0.8888888888

Factor a perfect square on the left side:
(y + -0.3333333334)(y + -0.3333333334) = -0.8888888888

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}