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m^{2}+m-2=0
To solve the inequality, factor the left hand side. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
m=\frac{-1±\sqrt{1^{2}-4\times 1\left(-2\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 1 for b, and -2 for c in the quadratic formula.
m=\frac{-1±3}{2}
Do the calculations.
m=1 m=-2
Solve the equation m=\frac{-1±3}{2} when ± is plus and when ± is minus.
\left(m-1\right)\left(m+2\right)>0
Rewrite the inequality by using the obtained solutions.
m-1<0 m+2<0
For the product to be positive, m-1 and m+2 have to be both negative or both positive. Consider the case when m-1 and m+2 are both negative.
m<-2
The solution satisfying both inequalities is m<-2.
m+2>0 m-1>0
Consider the case when m-1 and m+2 are both positive.
m>1
The solution satisfying both inequalities is m>1.
m<-2\text{; }m>1
The final solution is the union of the obtained solutions.