Factorise
$4 y^{3} + 20 y^{2} + 33 y + 18 = 0$

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Solution

$4 y^{3} + 20 y^{2} + 33 y + 18 = 0$

$= (y + 2) [\frac{4 y^{3} + 20 y^{2} + 33 y + 18}{(y + 2)}]$

$= (y + 2) [4 y^{2} + \frac{12 y^{2} + 33 y + 18}{(y + 2)}]$

$= (y + 2) [4 y^{2} + 12 y + \frac{9 y + 18}{(y + 2)}]$

$= (y + 2) (4 y^{2} + 12 y + 9)$

$= (y + 2) (2 y + 3) (2 y + 3)$

$= (y + 2) (2 y + 3)^{2}$

$y = 2, \frac{- 3}{2}$

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