Question
$$4x+2+(2x-3)(3x-2) = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 4 }+\dfrac{\sqrt{ 111 }}{ 12 }i & x_2 = \dfrac{ 3 }{ 4 }-\dfrac{\sqrt{ 111 }}{ 12 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4x+2+(2x-3)(3x-2) &= 0&& \text{simplify left side} \\[1 em]4x+2+6x^2-4x-9x+6 &= 0&& \\[1 em]4x+2+6x^2-13x+6 &= 0&& \\[1 em]6x^2-9x+8 &= 0&& \\[1 em] \end{aligned} $$
$ 6x^{2}-9x+8 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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