(4y-1)(5-y)=0

Solution for (4y-1)(5-y)=0 equation:

Simplifying
(4y + -1)(5 + -1y) = 0

Reorder the terms:
(-1 + 4y)(5 + -1y) = 0

Multiply (-1 + 4y) * (5 + -1y)
(-1(5 + -1y) + 4y * (5 + -1y)) = 0
((5 * -1 + -1y * -1) + 4y * (5 + -1y)) = 0
((-5 + 1y) + 4y * (5 + -1y)) = 0
(-5 + 1y + (5 * 4y + -1y * 4y)) = 0
(-5 + 1y + (20y + -4y2)) = 0

Combine like terms: 1y + 20y = 21y
(-5 + 21y + -4y2) = 0

Solving
-5 + 21y + -4y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 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 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Subproblem 2
Set the factor '(1 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 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 + -4y = 0 + -1

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

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

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Solution
y = {5, 0.25}