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

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

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

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

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

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

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

Solving
-12 + -4y + y2 = 0

Solving for variable 'y'.

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

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 + -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 = {-2, 6}