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

Solution for -2(y+3)(-y+6)=0 equation:

Simplifying
-2(y + 3)(-1y + 6) = 0

Reorder the terms:
-2(3 + y)(-1y + 6) = 0

Reorder the terms:
-2(3 + y)(6 + -1y) = 0

Multiply (3 + y) * (6 + -1y)
-2(3(6 + -1y) + y(6 + -1y)) = 0
-2((6 * 3 + -1y * 3) + y(6 + -1y)) = 0
-2((18 + -3y) + y(6 + -1y)) = 0
-2(18 + -3y + (6 * y + -1y * y)) = 0
-2(18 + -3y + (6y + -1y2)) = 0

Combine like terms: -3y + 6y = 3y
-2(18 + 3y + -1y2) = 0
(18 * -2 + 3y * -2 + -1y2 * -2) = 0
(-36 + -6y + 2y2) = 0

Solving
-36 + -6y + 2y2 = 0

Solving for variable 'y'.

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

Factor a trinomial.
2((-3 + -1y)(6 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
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

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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
Solution
y = {-3, 6}