Since the coordinate of any point of intersection has the form (a, f(a)) = (a, g(a)), these
points must make f(x) = g(x) true when x = a. In our example, we can tell from the graph
that both r=-1 and x = 8 are solutions to the original equation.
We can also use algebra to identify solutions to (r + 4) (x - 8) = (2 - x)(x - 8) by
rearranging and then recognizing that both parts have a factor of (x - 8) in common:
(X-4)(x-8)=(2-x)(x-8)
(X-4)(x-8)-(2-x)(x-8)=0
(X-8)(x+4-2+x)=0
(X-8)(2x+2)=0
X=8,-1
For polynomials created to model specific situations that have a more messy structure,
solving without using technology can be challenging, especially because the graphs of two
polynomials can intersect at multiple points because of the way they curve. Fortunately,
this type of solving challenge is one that computer algebra systems are usually very good
at, leaving the interpretation of the solution up to humans.