we have the equation
[tex]n^3+n^2-2n=0[/tex]step 1
Factor n
so
[tex]n\lbrack n^2+n-2\rbrack=0[/tex]Solve the quadratic equation, using the formula
we have
a=1
b=1
c=-2
substitute
[tex]n=\frac{-1\pm\sqrt[\square]{(1^2)-4(1)(-2)}}{2(1)}[/tex][tex]\begin{gathered} n=\frac{-1\pm\sqrt[\square]{9}}{2} \\ \\ n=\frac{-1\pm3}{2} \end{gathered}[/tex]the values of n are
n=1 and n=-2
therefore
[tex]n^3+n^2-2n=n(n+2)(n-1)[/tex]the values of n are
n=0
n=-2
n=1
