-5(y+6)(-y-2)=0

Solution for -5(y+6)(-y-2)=0 equation:

Simplifying
-5(y + 6)(-1y + -2) = 0

Reorder the terms:
-5(6 + y)(-1y + -2) = 0

Reorder the terms:
-5(6 + y)(-2 + -1y) = 0

Multiply (6 + y) * (-2 + -1y)
-5(6(-2 + -1y) + y(-2 + -1y)) = 0
-5((-2 * 6 + -1y * 6) + y(-2 + -1y)) = 0
-5((-12 + -6y) + y(-2 + -1y)) = 0
-5(-12 + -6y + (-2 * y + -1y * y)) = 0
-5(-12 + -6y + (-2y + -1y2)) = 0

Combine like terms: -6y + -2y = -8y
-5(-12 + -8y + -1y2) = 0
(-12 * -5 + -8y * -5 + -1y2 * -5) = 0
(60 + 40y + 5y2) = 0

Solving
60 + 40y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + 8y + y2) = 0

Factor a trinomial.
5((6 + y)(2 + y)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

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

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