y(2y^2-3y+6)=

Solution for y(2y^2-3y+6)= equation:

Simplifying
y(2y2 + -3y + 6) = 0

Reorder the terms:
y(6 + -3y + 2y2) = 0
(6 * y + -3y * y + 2y2 * y) = 0
(6y + -3y2 + 2y3) = 0

Solving
6y + -3y2 + 2y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(6 + -3y + 2y2) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(6 + -3y + 2y2)' equal to zero and attempt to solve:

Simplifying
6 + -3y + 2y2 = 0

Solving
6 + -3y + 2y2 = 0

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

Divide each side by '2'.
3 + -1.5y + y2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.5y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -1.5y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.5y + y2 = 0 + -3
-1.5y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.5y + y2 = -3

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = -3 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = -3 + 0.5625

Combine like terms: -3 + 0.5625 = -2.4375
0.5625 + -1.5y + y2 = -2.4375

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = -2.4375

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}