To determine whether an equation has one, none, or many solutions, we need to solve the equation for the variable. In the case of the equation 2(2x+-1)=4x-4, we can solve for x by first distributing the 2 on the left-hand side of the equation:
22x+2-1 = 4x - 4
This gives us the following equation:
4x-2 = 4x - 4
We can then subtract 4x from both sides of the equation to obtain:
-2 = -4
This equation does not have any solutions, because the left-hand side and the right-hand side are not equal. Therefore, the original equation has no solutions.