(y-1)(y-5)=0

Solution for (y-1)(y-5)=0 equation:

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

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

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

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

Combine like terms: -1y + -5y = -6y
(5 + -6y + y2) = 0

Solving
5 + -6y + y2 = 0

Solving for variable 'y'.

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Subproblem 2
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
Solution
y = {1, 5}