Answer
Zeros: $7,-2$
$x$-intercepts: $7,-2$
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 $H(x)=0$:
$$(2-x)^2+(2-x)-20=0$$
Let $u=2-x$, the original equation becomes
$$u^2+u-20=0$$
By factoring
$$(u+5)(u-4) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation ton obtain::
\begin{align*}
u +5&=0 &\text{ or }& &u-4=0\\
u &= -5 &\text{ or }& &u=4\\
\end{align*}
To solve for $x$, we use $u=2-x$
$$\because u = 2-x$$
$$\therefore x = 2-u$$
For $u=-5$
$$x=2-(-5) $$
$$x= 7$$
For $u=4$
$$x=2-4$$
$$x= -2$$
$\therefore x =7,-2$
