Finding all the zeroes of a discontinuous function in a particular range

I am trying to find the zeroes of the following symbolic function.

syms x 
moment =20*heaviside(x - 8)*(x - 8) - (3*x^2*heaviside(x))/4 + 5*heaviside(x - 20)*(x - 20) +... 
(3*heaviside(x - 20)*(x - 20)^2)/4; 
fplot(diff(moment,1),[-2 20])
solve(diff(moment,1) == 0, x, 'MaxDegree', 4);
extrema = vpa(ans, 6)
subs(moment,extrema) 

Matlabs outputs

extrema =
-1.0
ans =
0.0

However, the first derivative of the above moment function has a number of zeroes located at points other than -1, for example at approximately x = 13. Could someone please explain how all the zeroes or the zeroes in a particular range can be found?

Answer 1

[Star Strider]

It may be version-dependent.

In R2020b (Update 1), I get:

extrema = 
13.3333
   -1.0
 
ans =
-26.666666666666666666666666670975
                                 0

Plotting the function as well as the derivative:

figure
fplot(diff(moment,1),[-2 20])
hold on
fplot(moment,[-2 20])
hold off

supports those.

[Aleem Andrew]

Thank you for your answer

[Star Strider]

As always, my pleasure!