Solve the Quadratic Equation by Factorization: 9x² − 3x − 2 = 0

Question: Solve the following quadratic equation by factorization:

$$ 9x^2-3x-2=0 $$

Solution

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

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

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

Either

$$ 3x-2=0 $$

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

or

$$ 3x+1=0 $$

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

Hence,

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