$$3x^6+4x^5+3x^4+3x^2+2x+1 = 3x^6+4x^5+3x^4+3x^2+2x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3x^6+4x^5+3x^4+3x^2+2x+1 &= 3x^6+4x^5+3x^4+3x^2+2x&& \text{move all terms to the left hand side } \\[1 em]3x^6+4x^5+3x^4+3x^2+2x+1-3x^6-4x^5-3x^4-3x^2-2x &= 0&& \text{simplify left side} \\[1 em]3x^6+4x^5+3x^4+3x^2+2x+1-3x^6-4x^5-3x^4-3x^2-2x &= 0&& \\[1 em]1 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 1 = 0 } $ is FALSE, we conclude that the equation has no solution.
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