y(2y-1)=1

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

Simplifying
y(2y + -1) = 1

Reorder the terms:
y(-1 + 2y) = 1
(-1 * y + 2y * y) = 1
(-1y + 2y2) = 1

Solving
-1y + 2y2 = 1

Solving for variable 'y'.

Reorder the terms:
-1 + -1y + 2y2 = 1 + -1

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

Factor a trinomial.
(-1 + -2y)(1 + -1y) = 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 + -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 = {-0.5, 1}