$$2x^2+6x+1+3x^2+3x+9 = 5x^2+9x+10$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 2x^2+6x+1+3x^2+3x+9 &= 5x^2+9x+10&& \text{simplify left side} \\[1 em]5x^2+9x+10 &= 5x^2+9x+10&& \text{move all terms to the left hand side } \\[1 em]5x^2+9x+10-5x^2-9x-10 &= 0&& \text{simplify left side} \\[1 em]5x^2+9x+10-5x^2-9x-10 &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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