(y-2)(y-3)=0

Solution for (y-2)(y-3)=0 equation:

Simplifying
(y + -2)(y + -3) = 0

Reorder the terms:
(-2 + y)(y + -3) = 0

Reorder the terms:
(-2 + y)(-3 + y) = 0

Multiply (-2 + y) * (-3 + y)
(-2(-3 + y) + y(-3 + y)) = 0
((-3 * -2 + y * -2) + y(-3 + y)) = 0
((6 + -2y) + y(-3 + y)) = 0
(6 + -2y + (-3 * y + y * y)) = 0
(6 + -2y + (-3y + y2)) = 0

Combine like terms: -2y + -3y = -5y
(6 + -5y + y2) = 0

Solving
6 + -5y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + -1y)(3 + -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 '(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 = {2, 3}