$$9x^2-1 = (3x+1)(2x-3)$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 3 } & x_2 = -2 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 9x^2-1 &= (3x+1)(2x-3)&& \text{simplify right side} \\[1 em]9x^2-1 &= 6x^2-9x+2x-3&& \\[1 em]9x^2-1 &= 6x^2-7x-3&& \text{move all terms to the left hand side } \\[1 em]9x^2-1-6x^2+7x+3 &= 0&& \text{simplify left side} \\[1 em]3x^2+7x+2 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+7x+2 = 0 $ is a quadratic equation.
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