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

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

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

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

Multiply (-1 + 2y) * (1 + -2y)
(-1(1 + -2y) + 2y * (1 + -2y)) = 0
((1 * -1 + -2y * -1) + 2y * (1 + -2y)) = 0
((-1 + 2y) + 2y * (1 + -2y)) = 0
(-1 + 2y + (1 * 2y + -2y * 2y)) = 0
(-1 + 2y + (2y + -4y2)) = 0

Combine like terms: 2y + 2y = 4y
(-1 + 4y + -4y2) = 0

Solving
-1 + 4y + -4y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-1 + 2y = 0

Solving
-1 + 2y = 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 + 2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2y = 0 + 1
2y = 0 + 1

Combine like terms: 0 + 1 = 1
2y = 1

Divide each side by '2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0.5, 0.5}