(y-1)(y-3)=0

Solution for (y-1)(y-3)=0 equation:

Simplifying
(y + -1)(y + -3) = 0

Reorder the terms:
(-1 + y)(y + -3) = 0

Reorder the terms:
(-1 + y)(-3 + y) = 0

Multiply (-1 + y) * (-3 + y)
(-1(-3 + y) + y(-3 + y)) = 0
((-3 * -1 + y * -1) + y(-3 + y)) = 0
((3 + -1y) + y(-3 + y)) = 0
(3 + -1y + (-3 * y + y * y)) = 0
(3 + -1y + (-3y + y2)) = 0

Combine like terms: -1y + -3y = -4y
(3 + -4y + y2) = 0

Solving
3 + -4y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -1y)(3 + -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 '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {1, 3}