Y(y-3)(y+6)=0

Solution for Y(y-3)(y+6)=0 equation:

Simplifying
Y(y + -3)(y + 6) = 0

Reorder the terms:
Y(-3 + y)(y + 6) = 0

Reorder the terms:
Y(-3 + y)(6 + y) = 0

Multiply (-3 + y) * (6 + y)
Y(-3(6 + y) + y(6 + y)) = 0
Y((6 * -3 + y * -3) + y(6 + y)) = 0
Y((-18 + -3y) + y(6 + y)) = 0
Y(-18 + -3y + (6 * y + y * y)) = 0
Y(-18 + -3y + (6y + y2)) = 0

Combine like terms: -3y + 6y = 3y
Y(-18 + 3y + y2) = 0
(-18 * Y + 3y * Y + y2 * Y) = 0
(-18Y + 3yY + y2Y) = 0

Solving
-18Y + 3yY + y2Y = 0

Solving for variable 'Y'.

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

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

Factor a trinomial.
Y((-6 + -1y)(3 + -1y)) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Add 'y' to each side of the equation.
-1y + y = 6 + y

Combine like terms: -1y + y = 0
0 = 6 + y

Simplifying
0 = 6 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Add 'y' to each side of the equation.
-1y + y = -3 + y

Combine like terms: -1y + y = 0
0 = -3 + y

Simplifying
0 = -3 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
Y = {0}