$$w^2 = -11w$$
Answer
$$ \begin{matrix}w_1 = 0 & w_2 = -11 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} w^2 &= -11w&& \text{move all terms to the left hand side } \\[1 em]w^2+11w &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ x^{2}+11x = 0 } $, first we need to factor our $ x $.
$$ x^{2}+11x = x \left( x+11 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ x+11 = 0$.
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