Step-by-step explanation:
To start, every term has an
x
in common, so we can factor that out. Doing this, we get
x
(
x
2
+
x
−
42
)
=
0
What I have in blue can be factored by a thought experiment. What two numbers have a sum of
1
and a product of
−
42
?
After some trial and error, we arrive at
−
6
and
7
. Thus, this business can be factored as
x
(
x
−
6
)
(
x
+
7
)
=
0
We can leverage the zero product property here, setting all three terms equal to zero. As our zeroes, we get
x
=
0
,
x
=
6
, and
x
=
−
7
