Question
$$\frac{2x+5}{x-2}(x+1) = 0$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = -\dfrac{ 5 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2x+5}{x-2}(x+1) &= 0&& \text{simplify left side} \\[1 em]\frac{2x^2+7x+5}{x-2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-2 }. \\[1 em](x-2)\frac{2x^2+7x+5}{x-2} &= (x-2)\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2+7x+5 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+7x+5 = 0 $ is a quadratic equation.
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