We are given the function

we want to find all zeros of this function. That is, we want to find all value of x such that f(x) is zero. So, we have the following equation

Note that in this case the function f is a product of the following functions


and

so, since f is the product of these functions, for f to have the value of 0, at least one of this functions should be 0.
So we analyze each function separately.
Function 5x:
We have the following equation

By dividing both sides by 5, we get

so one zero is x=0.
Function (x-7)²:
We have the following equation:

Recall that the square of a number can be zero if and only if the number itself is zero. So we get

By adding 7 on both sides, we get

So another zero of the function is x=7.
Function (x-16)²:
We have the following equation:

Recall tha the square of a number can be zero if and only if the number itself is zero. So we get

By adding 16 on both sides, we get

so the last zero is 16.
In conclusion, the zeros of the function f are x=0, x=7 and x=16.