Importance of Base 10

Re-writing g(x) = 0, after transposing and putting x = 10, $4(a 10^5 + b 10^4 + c 10^3 + d 10^2 + e .10 + f ) = 3( d 10^5 + e 10^4 + f 10^3 + a 10^2 + b . 10 + c)$ $\large{\rightarrow 4 \overline{abcdef} = 3 \overline{defabc}}$ $\rightarrow 4000 \overline{ abc} +4 \overline{ def} = 3000 \overline{ def} + 3 \overline{ abc}$ $\rightarrow 3997 \overline{ abc} = 2996\overline{ def}$ $\rightarrow 571\overline{ abc} = 428 \overline{def.}$ It may be concluded from here that $\overline{abc} = 428$ and $\overline{ def} = 571.$ Hence a + b + c + d + e + f = 27.