2Y(Y+6)(Y-1)=0

Solution for 2Y(Y+6)(Y-1)=0 equation:

Simplifying
2Y(Y + 6)(Y + -1) = 0

Reorder the terms:
2Y(6 + Y)(Y + -1) = 0

Reorder the terms:
2Y(6 + Y)(-1 + Y) = 0

Multiply (6 + Y) * (-1 + Y)
2Y(6(-1 + Y) + Y(-1 + Y)) = 0
2Y((-1 * 6 + Y * 6) + Y(-1 + Y)) = 0
2Y((-6 + 6Y) + Y(-1 + Y)) = 0
2Y(-6 + 6Y + (-1 * Y + Y * Y)) = 0
2Y(-6 + 6Y + (-1Y + Y2)) = 0

Combine like terms: 6Y + -1Y = 5Y
2Y(-6 + 5Y + Y2) = 0
(-6 * 2Y + 5Y * 2Y + Y2 * 2Y) = 0
(-12Y + 10Y2 + 2Y3) = 0

Solving
-12Y + 10Y2 + 2Y3 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), '2Y'.
2Y(-6 + 5Y + Y2) = 0

Factor a trinomial.
2Y((-6 + -1Y)(1 + -1Y)) = 0

Ignore the factor 2.
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

Divide each side by '-1'.
Y = -6

Simplifying
Y = -6
Subproblem 3
Set the factor '(1 + -1Y)' equal to zero and attempt to solve:

Simplifying
1 + -1Y = 0

Solving
1 + -1Y = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1Y = 0 + -1
-1Y = 0 + -1

Combine like terms: 0 + -1 = -1
-1Y = -1

Divide each side by '-1'.
Y = 1

Simplifying
Y = 1
Solution
Y = {0, -6, 1}