Answer
Zeros: $-6,-5$
$x$-intercepts: $-6,-5$
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 $G(x)=0$:
$$(x+2)^2+7(x+2)+12=0$$
Let $u=x+2$, the original equation becomes
$$u^2+7u+12=0$$
By factoring
$$(u+4)(u+3) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
u+4 &= 0 &\text{ or }& &u+3=0\\
u &= -4 &\text{ or }& &u=-3\\
\end{align*}
To solve for $x$, we use $u=x+2$
$$\because u = x+2$$
$$\therefore x = u-2$$
For $u=-4$
$$x=-4-2 $$
$$x= -6$$
For $u=-3$
$$x=-3-2$$
$$x= -5$$
$\therefore x = -6,-5$
