Solve the following complex equation

Question

We need all complex numbers satisfying the following equation:

$z^4+4z^3+7z^2+6z+3=0$

Answer 1

HINT: factor the equation: $$z^4+4z^3+7z^2+6z+3=(z^2+az+b)(z^2+cz+d)=0$$ And then, determine what the coefficients $a, b, c, d$ must be to satisfy the equation.

Then: use the quadratic formula on each factor.