Step 1
Find two factors that when added gives us 11z and when multiplied give us 28z².
[tex]\begin{gathered} \text{These factors are 4z and 7z} \\ 4z+7z=11z \\ 4z(7z)=28z^2 \end{gathered}[/tex]
Step 2
Replace 11z with (4z+7z)
[tex]\begin{gathered} z^2+4z+7z+28=0 \\ \end{gathered}[/tex]
Factorize
[tex]\begin{gathered} (z^2+4z)(+7z+28)=0 \\ Find\text{ GCF in each bracket} \\ z(\frac{z^2}{z}+\frac{4z}{z})+7(\frac{7z}{7}+\frac{28}{7})=0 \\ z(z+4)+7(z+4)=0 \end{gathered}[/tex]
Therefore;
[tex]\begin{gathered} (z+4)(z+7)=0 \\ z+4=0;\text{ z=-4} \\ z+7=0;\text{ z=-7} \\ z=-4,z=-7 \end{gathered}[/tex]
Answer;
[tex]z=-4,z=-7[/tex]
