Solve for a:
$9 a^{2} - 24 a + 15 = 0$

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Solution

Given, $9 a^{2} - 24 a + 15 = 0$

$\Rightarrow$ $9 a^{2} - 15 a - 9 a + 15 = 0$

$\Rightarrow$ $3 a (3 a - 5) - 3 (3 a - 5) = 0$

$\Rightarrow$ $(3 a - 5) (3 a - 3) = 0$

$\Rightarrow$ $3 a - 5 = 0$ and $3 a - 3 = 0$

$∴$ $a = \frac{5}{3}$ and $a = \frac{3}{3} = 1$

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