Question
$$x^2+3 = 5x+3$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 5 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+3 &= 5x+3&& \text{move all terms to the left hand side } \\[1 em]x^2+3-5x-3 &= 0&& \text{simplify left side} \\[1 em]x^2+3-5x-3 &= 0&& \\[1 em]x^2-5x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ x^{2}-5x = 0 } $, first we need to factor our $ x $.
$$ x^{2}-5x = x \left( x-5 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ x-5 = 0$.
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