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

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

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

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

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

Multiply (6 + y) * (2 + -1y)
3(6(2 + -1y) + y(2 + -1y)) = 0
3((2 * 6 + -1y * 6) + y(2 + -1y)) = 0
3((12 + -6y) + y(2 + -1y)) = 0
3(12 + -6y + (2 * y + -1y * y)) = 0
3(12 + -6y + (2y + -1y2)) = 0

Combine like terms: -6y + 2y = -4y
3(12 + -4y + -1y2) = 0
(12 * 3 + -4y * 3 + -1y2 * 3) = 0
(36 + -12y + -3y2) = 0

Solving
36 + -12y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -4y + -1y2) = 0

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

Ignore the factor 3.
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 '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

Simplifying
y = -6
Solution
y = {2, -6}