\left\{ \begin{array} { l } { a = ( n + b ) ( n + 4 ) ( n + 2 ) n } \\ { b = ( n + 4 ) ( n + 2 ) n } \\ { e = ( n + 2 ) n } \\ { d = a - 3 b n + 6 c n ^ { 2 } - 3 n ^ { 4 } + n ^ { 4 } } \end{array} \right.
Solve for a, n, b, d, c
a=\left(\sqrt{e+1}+1\right)\left(\sqrt{e+1}+3\right)\left(\left(\sqrt{e+1}-1\right)\left(\sqrt{e+1}+2\right)\right)^{2}\approx 191.901055093\text{, }n=\sqrt{e+1}-1\approx 0.928284686\text{, }b=\left(e+1\right)^{\frac{3}{2}}-\sqrt{e+1}+3e\approx 13.396466706\text{, }d=\left(\sqrt{e+1}-1\right)\left(6\sqrt{e+1}c-6c+e^{2}\sqrt{e+1}+17e\sqrt{e+1}-3\sqrt{e+1}-5\left(e+1\right)^{\frac{3}{2}}+7e^{2}+16e+8\right)\text{, }c\in \mathrm{R}
a=\left(-\sqrt{e+1}+1\right)\left(-\sqrt{e+1}+3\right)\left(\left(-\sqrt{e+1}+2\right)\left(\sqrt{e+1}+1\right)\right)^{2}\approx -0.043874384\text{, }n=-\sqrt{e+1}-1\approx -2.928284686\text{, }b=\sqrt{e+1}-\left(e+1\right)^{\frac{3}{2}}+3e\approx 2.913224265\text{, }d=12\sqrt{e+1}c+6ec+12c-4e^{2}\sqrt{e+1}-2e\left(e+1\right)^{\frac{3}{2}}-25e\sqrt{e+1}+23\left(e+1\right)^{\frac{3}{2}}-39\sqrt{e+1}+6e^{2}+e^{3}-12e-16\text{, }c\in \mathrm{R}
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