(y-5)(y-4)=0

Solution for (y-5)(y-4)=0 equation:

Simplifying
(y + -5)(y + -4) = 0

Reorder the terms:
(-5 + y)(y + -4) = 0

Reorder the terms:
(-5 + y)(-4 + y) = 0

Multiply (-5 + y) * (-4 + y)
(-5(-4 + y) + y(-4 + y)) = 0
((-4 * -5 + y * -5) + y(-4 + y)) = 0
((20 + -5y) + y(-4 + y)) = 0
(20 + -5y + (-4 * y + y * y)) = 0
(20 + -5y + (-4y + y2)) = 0

Combine like terms: -5y + -4y = -9y
(20 + -9y + y2) = 0

Solving
20 + -9y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
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 = {4, 5}