Can anybody resolve this pls.: Given that the complex number z = -2 + 7i is a root to the equation:

z^3 + 6 z^2 + 61 z + 106 = 0 find the real root to the equation

Another root will be z = -2 - 7i

So two factors will be (z + 2 - 7i) and (z + 2 + 7i)

Multiply them together and you get z^2 + 4z + 53

Now divide z^3 + 6z^2 + 61z + 106 by z^2 + 4z + 53
Quotient = z + 2

SOLUTION: The real root = -2

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multiply (z-(-2+7i)) and (z-(-2-7i)) to get z^2+4z+53
divide your original polynomial by this polynomial.
the result is z+2
therefore your real root is -2