Question
$$(2x+5)(3x+2) = -2$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 19 }{ 12 }-\dfrac{\sqrt{ 73 }}{ 12 } & x_2 = -\dfrac{ 19 }{ 12 }+\dfrac{\sqrt{ 73 }}{ 12 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (2x+5)(3x+2) &= -2&& \text{simplify left side} \\[1 em]6x^2+4x+15x+10 &= -2&& \\[1 em]6x^2+19x+10 &= -2&& \text{move all terms to the left hand side } \\[1 em]6x^2+19x+10+2 &= 0&& \text{simplify left side} \\[1 em]6x^2+19x+12 &= 0&& \\[1 em] \end{aligned} $$
$ 6x^{2}+19x+12 = 0 $ is a quadratic equation.
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