please i really need help

To factor this:

2z² - 11z - 21

Split the middle term.

What two numbers add to -11 and multiply to (-21)(2)= -42 ? → -14 and 3

2z² - 14z + 3z - 21

(2z² - 14z) + (3z - 21)

Factor a 2z out of the first term and factor a 3 out of the second term.

2z(z - 7) + 3(z - 7)

Factor a (z - 7) out of both terms.

(2z + 3)(z - 7)

2z^2-11z-21

\(2z^2-11z-21\)

\(z = {11 \pm \sqrt{121+168} \over 4}=\frac{11\pm 17}{4}\)

\(z_1=7\\z_2=-1.5\)

\(2z^2-11z-21=2 \times(z-7)\times (z+1.5)\)

  !