Solve the following quadratic equation by factorization:
$6x^2\ +\ 11x\ +\ 3\ =\ 0$

Given:

Given quadratic equation is $6x^2\ +\ 11x\ +\ 3\ =\ 0$.

To do:

We have to solve the given quadratic equation by factorization. 

Solution:

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

$6x^2+9x+2x+3=0$ 

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

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

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

$3x=-1$ or $2x=-3$

$x=\frac{-1}{3}$ or $x=\frac{-3}{2}$

The roots of the given quadratic equation are $\frac{-1}{3}$ and $\frac{-3}{2}$.