(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 = -8y
(12 + -8y + y2) = 0

Solving
12 + -8y + 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}