Let's solve the equation step by step:

First distribute the 2 on the inside of the parentheses:
2(x-1) + 3 = 0.8x + 5.96

Now distribute the 1.2 on the left side of the equation:
2x - 2 + 3 = 0.8x + 5.96

Combine like terms:
2x + 1 = 0.8x + 5.96

Move all x terms to one side and constants to the other side:
2x - 0.8x = 5.96 - 1
1.2x = 4.96

Solve for x:
x = 4.96 / 1.2
x = 4.1333

So the solution to the equation 2(x-1) + 3 = 0.8x + 5.96 is x = 4.1333.