Factorise the following using a suitable method and verify the answer.
$6 x y - 4 y + 6 = 9 x$ .

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Solution

$\begin{matrix} 6 x y - 4 y + 6 = 9 x \Rightarrow 6 x y - 4 y + 6 - 9 x = 0 \Rightarrow 6 x y - 9 x + (6 - 4 y) \Rightarrow 3 x (2 y - 3) - 2 (2 y - 2) = 0 \Rightarrow (3 x - 2) (2 y - 3) = 0 x = \frac{2}{3} a n d y = \frac{3}{2} S a t i s f y t h e e q^{n} P u t x = \frac{2}{3} a n d y = \frac{3}{2} 6 \times \frac{2}{3} \times \frac{3}{2} y \times \frac{3}{2} + 6 = 9 \times \frac{2}{3} 6 - 6 + 6 = 6 6 = 6 T r u e A n s . \end{matrix}$

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