$$(2x+9)(x-6) = 6x+27$$
Answer
$$ \begin{matrix}x_1 = 9 & x_2 = -\dfrac{ 9 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (2x+9)(x-6) &= 6x+27&& \text{simplify left side} \\[1 em]2x^2-12x+9x-54 &= 6x+27&& \\[1 em]2x^2-3x-54 &= 6x+27&& \text{move all terms to the left hand side } \\[1 em]2x^2-3x-54-6x-27 &= 0&& \text{simplify left side} \\[1 em]2x^2-9x-81 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-9x-81 = 0 $ is a quadratic equation.
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