We are given:

4x² + 4y² − 4xy − 6y + 3

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Step 1: Group terms
= (4x² + y² − 4xy) + (3y² − 6y + 3)

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Step 2: Simplify
4x² + y² − 4xy = (2x − y)²  
3y² − 6y + 3 = 3(y² − 2y + 1) = 3(y − 1)²  

So,  
4x² + 4y² − 4xy − 6y + 3 = (2x − y)² + 3(y − 1)²

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Step 3: Solve
Equation: (2x − y)² + 3(y − 1)² = 0  

A sum of squares is zero only if each term = 0:  
(2x − y)² = 0  ⇒  2x = y  
3(y − 1)² = 0  ⇒  y = 1  

So, y = 1 and x = 1/2  

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Step 4: Find required value
(4x + 5y) = 4(1/2) + 5(1)  
           = 2 + 5  
           = 7  

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Final Answer:
7