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Algebra Level 4

Find all ordered pairs of real numbers $(a, b)$ such that ${ (x-a) }^{ 2 }+{ (2x-b) }^{ 2 }={ (x-3) }^{ 2 }+{ (2x) }^{ 2 }$ is true for all values of $x$ .

Let $n$ be the sum of all $a$ 's in ordered pair $(a, b)$ and $m$ be the sum of all $b$ 's in the ordered pair $(a, b)$ .