Solve by factoring
2
z
2
−
27
z
+
13
=
0
Split the middle term
Split the middle term into two terms
2
z
2
−
26
z
−
z
+
13
=
0
2
z
2
−
26
z
−
z
+
13
=
0
Factorize
Factor the first two terms and the last two terms separately
2
z
(
z
−
13
)
−
(
z
−
13
)
=
0
2
z
(
z
−
13
)
−
(
z
−
13
)
=
0
Factor out
Factor out
(
z
−
13
)
(
2
z
−
1
)
=
0
(
z
−
13
)
(
2
z
−
1
)
=
0
Apply Zero Product Property
Apply Zero Product Property
z
−
13
=
0
or
2
z
−
1
=
0
2
z
−
1
=
0
or
z
−
13
=
0
More steps
Show more steps
2
z
−
1
=
0
Rearrange variables to the left side of the equation
2
z
=
1
Divide both sides of the equation by the coefficient of variable
z
=
2
1
Divide both sides of the equation by the coefficient of variable
z
=
2
1
z
−
13
=
0
Rearrange variables to the left side of the equation
z
=
13
z
=
13
or
z
=
2
1
Answer
z
=
13
or
z
=
2
1