A graph shows that there are only two real zeroes, the other two being complex.
The graph shows that x=-2.1441 approx and 1.6327 approx.
To find the complex zeroes, first construct one quadratic from the two zeroes above and then divide the quartic by this quadratic to find the other quadratic, which will have real coefficients. Use the quadratic formula to find the complex zeroes (conjugates).