a) \(x^3+15x^2+75x=-125\)
\(\Leftrightarrow x^3+15x^2+75x+125=0\)
\(\Leftrightarrow x^3+125+15x^2+75x=0\)
\(\Leftrightarrow\left(x+5\right)\left(x^2+5x+25\right)+15x\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x^2+20x+25\right)=0\)
\(TH1:x+5=0\Leftrightarrow x=-5\)
\(TH2:x^2+20x+25=0\)
\(\Leftrightarrow\left(x+10\right)^2=75\)
\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{75}-10\\x=-\sqrt{75}-10\end{cases}}\)
b) \(x\left(x-3\right)\left(x+3\right)-\left(x+2\right)\left(x^2-2x+4\right)=10\)
\(\Leftrightarrow x\left(x^2-9\right)-\left(x^3+8\right)=10\)
\(\Leftrightarrow x^3-9x-x^3-8=9\)
\(\Leftrightarrow-9x=17\)
\(\Leftrightarrow x=\frac{-17}{9}\)
