Question
$$(a-\frac{1}{7})(a-\frac{1}{5}) = 0$$
Answer
$$ \begin{matrix}a_1 = \dfrac{ 1 }{ 5 } & a_2 = \dfrac{ 1 }{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (a-\frac{1}{7})(a-\frac{1}{5}) &= 0&& \text{simplify left side} \\[1 em]\frac{7a-1}{7}\frac{5a-1}{5} &= 0&& \\[1 em]\frac{35a^2-12a+1}{35} &= 0&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35 \cdot \frac{35a^2-12a+1}{35} &= 35\cdot0&& \text{cancel out the denominators} \\[1 em]35a^2-12a+1 &= 0&& \\[1 em] \end{aligned} $$
$ 35x^{2}-12x+1 = 0 $ is a quadratic equation.
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