How can one find the points of intersections of the two graphs algebraically?
$$f(x) = |(x-1)^2-4|$$
$$f(x) = |x+3|-2$$
I understand that it could be solved graphically and through some sort of system of piecewise functions,
$$f(x) = $$ \begin{cases} (x-1)^2-4, & \text{if $x \le -1$ or $x \ge 3$ } \\ -(x-1)^2+4|, & \text{if $-1\lt x \lt 3$} \end{cases}
$$g(x) = $$ \begin{cases} x+1, & \text{if $x \ge -3$} \\ -x-5, & \text{if $x \lt -3$} \end{cases}
but is there a clean algebraic way to solve it?