$$\frac{3}{2}y^2+\frac{11}{10}y = 0$$
Answer
$$ \begin{matrix}y_1 = 0 & y_2 = -\dfrac{ 11 }{ 15 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{2}y^2+\frac{11}{10}y &= 0&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{3}{2}y^2+10\frac{11}{10}y &= 10\cdot0&& \text{cancel out the denominators} \\[1 em]15y^2+11y &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 15x^{2}+11x = 0 } $, first we need to factor our $ x $.
$$ 15x^{2}+11x = x \left( 15x+11 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 15x+11 = 0$.
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