Answer
Zeros: $-\dfrac{7}{2},-1$
$x$-intercepts: $-\dfrac{7}{2},-1$
Work Step by Step
To find the zeros of a function $f$, solve the equation $f(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $f(x)=0$:
$$(2x+5)^2-(2x+5)-6=0$$
Let $u=2x+5$, the original equation becomes
$$u^2-u-6=0$$
By factoring
$$(u+2)(u-3) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
u+2 &= 0 &\text{ or }& &u=3\\
u &= -2 &\text{ or }& &u=3\\
\end{align*}
To solve for $x$, we use $u=2x+5$
$$\because u = 2x+5$$
$$\therefore 2x = u-5$$
$$\therefore x = \dfrac{u-5}{2}$$
For $u=-2$
$$x=\dfrac{-2-5}{2} $$
$$x= -\dfrac{7}{2}$$
For $u=3$
$$x=\dfrac{3-5}{2}$$
$$x= -1$$
$\therefore x = -\dfrac{7}{2},-1$
