$$(3x-1)(4x+7)-(4x+7)(5x-2) = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 2 } & x_2 = -\dfrac{ 7 }{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (3x-1)(4x+7)-(4x+7)(5x-2) &= 0&& \text{simplify left side} \\[1 em]12x^2+21x-4x-7-(20x^2-8x+35x-14) &= 0&& \\[1 em]12x^2+17x-7-(20x^2+27x-14) &= 0&& \\[1 em]12x^2+17x-7-20x^2-27x+14 &= 0&& \\[1 em]-8x^2-10x+7 &= 0&& \\[1 em] \end{aligned} $$
$ -8x^{2}-10x+7 = 0 $ is a quadratic equation.
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