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Solve for $x: 6 x^2+11 x+3=0$.

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SOLUTION —

$6 x^2+11 x+3=0$

$\Rightarrow 6 x^2+9 x+2 x+3=0$

$\Rightarrow 3 x(2 x+3)+1(2 x+3)=0$

$\Rightarrow(2 x+3)(3 x+1)=0$

$\Rightarrow 2 x+3=0$ or $3 x+1=0$

i.e., $x=-\frac{3}{2}$ or, $x=-\frac{1}{3}$

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