Solve:
${12 x}^{2} + 25 x + 12 = 0$

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Solution

$12 x^{2} + 25 x + 12 = 0$
$\Rightarrow 12 x^{2} + 16 x + 9 x + 12 = 0$
$\Rightarrow 4 x (3 x + 4) + 3 (3 x + 4) = 0$
$\Rightarrow (3 x + 4) (4 x + 3) = 0$
$∴ x = \frac{- 4}{3}, \frac{- 3}{4}$

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6 x^{4} - 25 x^{3} + 12 x^{2} + 25 x + 6 = 0

6 x^{4} - 25 x^{3} + 12 x^{2} + 25 x + 6 = 0

Factories:

$12 x^{2} - 25 x + 12$

\frac{6 x^{2} - x - 2}{8 x^{2} + 6 x + 1} \times \frac{12 x^{2} - 13 x - 4}{12 x^{2} - 25 x + 12}

6 x^{4} - 25 x^{3} + 12 x^{2} + 25 x + 6 = 0

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