1 Simplify
n
(
n
−
1
)
(
n
−
2
)
×
1
n(n−1)(n−2)×1 to
n
(
n
−
1
)
(
n
−
2
)
n(n−1)(n−2)
n
=
n
(
n
−
1
)
(
n
−
2
)
n=n(n−1)(n−2)
2 Expand
n
=
n
3
−
2
n
2
−
n
2
+
2
n
n=n
3
−2n
2
−n
2
+2n
3 Simplify
n
3
−
2
n
2
−
n
2
+
2
n
n
3
−2n
2
−n
2
+2n to
n
3
−
3
n
2
+
2
n
n
3
−3n
2
+2n
n
=
n
3
−
3
n
2
+
2
n
n=n
3
−3n
2
+2n
4 Move all terms to one side
n
−
n
3
+
3
n
2
−
2
n
=
0
n−n
3
+3n
2
−2n=0
5 Simplify
n
−
n
3
+
3
n
2
−
2
n
n−n
3
+3n
2
−2n to
−
n
−
n
3
+
3
n
2
−n−n
3
+3n
2
−
n
−
n
3
+
3
n
2
=
0
−n−n
3
+3n
2
=0
6 Factor out the common term
n
n
−
n
(
1
+
n
2
−
3
n
)
=
0
−n(1+n
2
−3n)=0
7 Multiply both sides by
−
1
−1
n
(
1
+
n
2
−
3
n
)
=
0
n(1+n
2
−3n)=0
8 Solve for
n
n
n
=
0
n=0
9 Apply the Quadratic FormulaHow?
n
=
3
+
5
2
,
3
−
5
2
n=
2
3+√
5
,
2
3−√
5
10 Collect all solutions from the previous steps
n
=
0
,
3
+
5
2
,
3
−
5
2
n=0,
2
3+√
5
,
2
3−√
5
Done
