(y-1)(y-4)=0

Solution for (y-1)(y-4)=0 equation:

Simplifying
(y + -1)(y + -4) = 0

Reorder the terms:
(-1 + y)(y + -4) = 0

Reorder the terms:
(-1 + y)(-4 + y) = 0

Multiply (-1 + y) * (-4 + y)
(-1(-4 + y) + y(-4 + y)) = 0
((-4 * -1 + y * -1) + y(-4 + y)) = 0
((4 + -1y) + y(-4 + y)) = 0
(4 + -1y + (-4 * y + y * y)) = 0
(4 + -1y + (-4y + y2)) = 0

Combine like terms: -1y + -4y = -5y
(4 + -5y + y2) = 0

Solving
4 + -5y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -1y)(4 + -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 '(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
Solution
y = {1, 4}