f(x) = 0 is the same as saying y = 0. When y = 0, the line will cross the x-axis. Look for where the line crosses the x-axis.
The line crosses the x-axis at x = -1, x = 0, and x = 8. At these x-points, y will equal 0.
The answer is 'When f(x) = 0, x = -1, 0, -8.'
