$$\frac{2}{c-5} = \frac{c}{2c+5}$$
Answer
$$ \begin{matrix}c_1 = -1 & c_2 = 10 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{c-5} &= \frac{c}{2c+5}&& \text{multiply ALL terms by } \color{blue}{ (c-5)(2c+5) }. \\[1 em](c-5)(2c+5)\cdot\frac{2}{c-5} &= (c-5)(2c+5)\frac{c}{2c+5}&& \text{cancel out the denominators} \\[1 em]4c+10 &= c^2-5c&& \text{move all terms to the left hand side } \\[1 em]4c+10-c^2+5c &= 0&& \text{simplify left side} \\[1 em]-c^2+9c+10 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+9x+10 = 0 $ is a quadratic equation.
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