X^2-7x+10=0 it says to “solve each equation by factoring and using the zero product rule

To factor this, you are looking for factors of 10 that add to -7.
.. 10 = -1*-10 = -2*-5
The latter two factors add to -7, so we can use them to write the factored form.
.. (x -2)(x -5) = 0

The Zero Product Rule says that if a product is zero, at least one of the factors must be zero.
.. x -2 = 0 . . . . . first factor is zero
.. x = 2

.. x -5 = 0 . . . . . second factor is zero
.. x = 5

The two solutions are x=2 or x=5.