$$\frac{2r}{10} = \frac{-1}{r+6}$$
Answer
$$ \begin{matrix}r_1 = -1 & r_2 = -5 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2r}{10} &= \frac{-1}{r+6}&& \text{multiply ALL terms by } \color{blue}{ 10(r+6) }. \\[1 em]10(r+6)\frac{2r}{10} &= 10(r+6)\cdot\frac{-1}{r+6}&& \text{cancel out the denominators} \\[1 em]2r^2+12r &= -10&& \text{move all terms to the left hand side } \\[1 em]2r^2+12r+10 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+12x+10 = 0 $ is a quadratic equation.
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