Question

-13^2(5x+10)(x-3)

how is 0, 0 a zero?

Answer 1

A "zero" of a function is an x-value where the function equals 0 (points on the x-axis). Your function is

f(x) = -13^2(5x+10)(x-3).

By order of operations -13^2 = -(13^2) = -169, so
f(x) = -169(5x+10)(x-3) = -169·5(x+2)(x-3) = -845(x+2)(x-3).

Set each factor equal to zero to find zeros:
5x+10 = 0 → x = -2,
x-3 = 0 → x = 3.

So the zeros are x = -2 and x = 3 (points (-2,0) and (3,0)).

(0,0) is not a zero because f(0) ≠ 0:
f(0) = -169(5·0+10)(0-3) = -169·10·(-3) = 5070.

If you wanted (0,0) to be a zero, the expression would need a factor x (for example x(5x+10)(x-3)).