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

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

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

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

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

Multiply (-5 + y) * (-6 + y)
(-5(-6 + y) + y(-6 + y)) = 0
((-6 * -5 + y * -5) + y(-6 + y)) = 0
((30 + -5y) + y(-6 + y)) = 0
(30 + -5y + (-6 * y + y * y)) = 0
(30 + -5y + (-6y + y2)) = 0

Combine like terms: -5y + -6y = -11y
(30 + -11y + y2) = 0

Solving
30 + -11y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(6 + -1y) = 0

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
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 = {5, 6}