To solve this equation, we can start by combining like terms:

0.5y(2y-1) - (0.5 - 2y) + 1 = 0
y^2 - 0.5y - 0.5 + 2y + 1 = 0
y^2 + 1.5y + 0.5 = 0

Next, we can simplify by multiplying the entire equation by 2 to get rid of the decimals:

2(y^2 + 1.5y + 0.5) = 0
2y^2 + 3y + 1 = 0

Now we can solve for y using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 3, and c = 1:

y = (-3 ± √(3^2 - 421)) / 2*2
y = (-3 ± √(9 - 8)) / 4
y = (-3 ± √1) / 4
y = (-3 ± 1) / 4

There are two possible solutions:

y = (-3 + 1) / 4 = -2 / 4 = -0.5y = (-3 - 1) / 4 = -4 / 4 = -1

So the solutions to the equation are y = -0.5 and y = -1.