Question

What are the x-intercept(s) of the graph of y − 8 = x2 − 6x?

Answer 1

x intercept means, it crosses X-axis i.e., y=0
substitute y=0 in the equation and solve for "x"
there will be 2 values.

Answer 2

exactly...so after doing as what @electrokid has said

0 - 8 = x² - 6x
-8 = x² - 6x
add 8 to both sides

x² - 6x + 8 = 0

now factor this...what 2 numbers multiply to equal 8...and at the same time add to become -6? 4 and 2 sound like a good fit

(x - 4)(x - 2)

lets check it

x² -2x -4x +8
x² - 6x + 8

indeed ...so ...using what we now have

(x - 4)(x - 2)

what makes these = 0?

? - 4 = 0?
? - 2 = 0?