(1-y)(2y-5)=0

Solution for (1-y)(2y-5)=0 equation:

Simplifying
(1 + -1y)(2y + -5) = 0

Reorder the terms:
(1 + -1y)(-5 + 2y) = 0

Multiply (1 + -1y) * (-5 + 2y)
(1(-5 + 2y) + -1y * (-5 + 2y)) = 0
((-5 * 1 + 2y * 1) + -1y * (-5 + 2y)) = 0
((-5 + 2y) + -1y * (-5 + 2y)) = 0
(-5 + 2y + (-5 * -1y + 2y * -1y)) = 0
(-5 + 2y + (5y + -2y2)) = 0

Combine like terms: 2y + 5y = 7y
(-5 + 7y + -2y2) = 0

Solving
-5 + 7y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + 2y)(1 + -1y) = 0

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

Simplifying
-5 + 2y = 0

Solving
-5 + 2y = 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 + 2y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2y = 0 + 5
2y = 0 + 5

Combine like terms: 0 + 5 = 5
2y = 5

Divide each side by '2'.
y = 2.5

Simplifying
y = 2.5
Subproblem 2
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
Solution
y = {2.5, 1}