Question
$$4(x+3)^2+3(x+3)-3 = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 27 }{ 8 }-\dfrac{\sqrt{ 57 }}{ 8 } & x_2 = -\dfrac{ 27 }{ 8 }+\dfrac{\sqrt{ 57 }}{ 8 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4(x+3)^2+3(x+3)-3 &= 0&& \text{simplify left side} \\[1 em]4(x^2+6x+9)+3(x+3)-3 &= 0&& \\[1 em]4x^2+24x+36+3x+9-3 &= 0&& \\[1 em]4x^2+27x+45-3 &= 0&& \\[1 em]4x^2+27x+42 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+27x+42 = 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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