This equation can be simplified by using the properties of absolute value and factoring.

Given the equation |2x+y-3| + 4x^2 - 4xy + y^2 = 0

First, notice that the expression inside the absolute value can be factored as (2x + y - 3).

So, the equation can be rewritten as |2x+y-3| + (2x - 3)(2x - 3) = 0

Now, since the absolute value expression is always non-negative, it must equal zero for the overall equation to hold true. Therefore, we have:

2x + y - 3 = 0
=> y = -2x + 3

Now, substituting y = -2x + 3 into the second part of the equation:

(2x - 3)(2x - 3) = 0
=> (2x - 3)^2 = 0
=> 2x - 3 = 0
=> 2x = 3
=> x = 3/2

Lastly, substitute x = 3/2 back into y = -2x + 3:

y = -2(3/2) + 3
=> y = -3 + 3
=> y = 0

Therefore, the solution to the equation is x = 3/2 and y = 0.