Answer
$x=-2, 4$
Work Step by Step
With $f(x)=11$, substitute $11$ to $f(x)$ to obtain:
$$\begin{align*}
11&=x^2-2x+3
\end{align*}$$
Subtract $11$ from each side:
$$
\begin{align*}
11-11&=x^2-2x+3-11\\
0&=x^2-2x-8
\end{align*}$$
Factor the trinomial by looking for factors of $-8$ whose sum is $-2$ (this yields $-4$ and $2$) to obtain:
$$0=(x-4)(x+2)$$
Solve the equation using the Zero-Product Property by equating each factor to zero, then solving each equation:
$$\begin{align*}
x-4&=0 &\text{or}& &x+2=0\\
x&=4 &\text{or}& &x=-2
\end{align*}$$
Therefore, the solutions are $-2$ and $4$.
