Question
$$(x-2)(x+3) = 4$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 41 }}{ 2 } & x_2 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 41 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x-2)(x+3) &= 4&& \text{simplify left side} \\[1 em]x^2+3x-2x-6 &= 4&& \\[1 em]x^2+x-6 &= 4&& \text{move all terms to the left hand side } \\[1 em]x^2+x-6-4 &= 0&& \text{simplify left side} \\[1 em]x^2+x-10 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+x-10 = 0 $ is a quadratic equation.
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