How do computer programs looks for polynomial's complex roots ?

For example the polynomials below have complex roots :

0.454*x^6+23.172*x^5
-12.33*x^4
+123.22*x^3+1.32*x^2
+122*x-642.22=0

0.874*x^6+12.143*x^5
-9.23*x^4
+982.432*x^3+3.31*x^2
+82.7*x-32.22=0

What algorithm should be used to search for the complex roots ?
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