Solve (x^2+x+m)^2geq(x^2-3x-m)^2

$$( x ^ { 2 } + x + m ) ^ { 2 } \geq ( x ^ { 2 } - 3 x - m ) ^ { 2 }$$

Solve for x

$$\left\{\begin{matrix}\\x=-\frac{m}{2}\text{; }x=1\text{, }&\text{unconditionally}\\x=0\text{, }&m\neq 0\\x\geq 1\text{, }&m\geq -2\\x\in [0,\infty)\cup [-\frac{m}{2},1]\text{, }&m=-2\\x\in [-\frac{m}{2},\infty)\cup [0,1]\text{, }&m\leq -2\\x\in [-\frac{m}{2},0]\text{, }&m\geq 0\\x\in [0,-\frac{m}{2}]\text{, }&m\geq -2\text{ and }m\leq 0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}\\m=-2x\text{, }&\text{unconditionally}\\m\geq -2x\text{, }&x\geq 1\text{ or }x\leq 0\\m\in \mathrm{R}\text{, }&x=0\text{ or }x=1\\m\leq -2x\text{, }&x\geq 0\text{ and }x\leq 1\end{matrix}\right.$$