Question
$$x^2+1 = 3x^2+2x+1$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+1 &= 3x^2+2x+1&& \text{move all terms to the left hand side } \\[1 em]x^2+1-3x^2-2x-1 &= 0&& \text{simplify left side} \\[1 em]x^2+1-3x^2-2x-1 &= 0&& \\[1 em]-2x^2-2x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -2x^{2}-2x = 0 } $, first we need to factor our $ x $.
$$ -2x^{2}-2x = x \left( -2x-2 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ -2x-2 = 0$.
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