Solve the Quadratic Equation by Factorization: 6x² + 11x + 3 = 0

Question: Solve the following quadratic equation by factorization:

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

Solution

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

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

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

Either

$$ 2x+3=0 $$

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

or

$$ 3x+1=0 $$

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

Hence,

$$ \boxed{x=-\frac{3}{2},\ -\frac{1}{3}} $$