QUBO to PUBO?

If I try to transform a PUBO
x_0 x_1 x_2

to QUBO, certain documentation says that I need to add the constraint
6 x_3 + 2 x_0 x_1 - 4 x_0 x_3 - 4 x_1 x_3

However, I need to arrive to a minima (there in this case 0) or a maxima (in this case 1)

Usually, I use a function to minimize so I negate my cost function to get a maxima.

But with the above cost function and constraint, I am not arriving anywhere to get a minima or a maxima with the same cost function + constraint (changing sign accordingly)

Any idea?