We're able to discharge directly into our backyard but we have a VERY big backyard, more than an acre. Friends of ours dug a very shallow trench, laid PVC pipe connected to an upright, and discharge into a low spot of their backyard via what looks like a splashy fountain. Another friend discharges backwash/waste down his driveway from where it runs into a sewer grate.

The laundry sink is probably not going to be able to handle it because its drain is smaller than the inflow hose.