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

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

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

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

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

Multiply (6 + 3y) * (-6 + 2y)
(6(-6 + 2y) + 3y * (-6 + 2y)) = 0
((-6 * 6 + 2y * 6) + 3y * (-6 + 2y)) = 0
((-36 + 12y) + 3y * (-6 + 2y)) = 0
(-36 + 12y + (-6 * 3y + 2y * 3y)) = 0
(-36 + 12y + (-18y + 6y2)) = 0

Combine like terms: 12y + -18y = -6y
(-36 + -6y + 6y2) = 0

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

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + -1y + y2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
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
Solution
y = {-2, 3}