<s>[INST] How to solve the cubic equation $x^3-12x+16=0$ Please help me for solving this equation $x^3-12x+16=0$
 [/INST] HINT: 

$$
\begin{align*}
x^3-12x-16&=x\underbrace{(x^2-4)}_{(x-2)(x+2)}-8x-16 \tag{1}\\
&=x(x-2)(x+2)-\underbrace{8x-16}_{-8(x+2)}\\
&=(x+2) \underbrace{(x^2-2x-8)}_{\text{quadratic equation}}=0 
\\
\end{align*}$$

Now just solve the quadratic equation and you should get something like:
$$(x+2)(x+a)(x+b)=0\tag{2}$$
and find:  $\,\,x=-2,x=-a \,\,\text{or}\,\,x=-b$
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