(x+a)(x+b+ci)(x+bci)(x+a)(x+b+ci)(x+b-ci)

Algebra Level 2

Suppose that a,b,ca, b, c are positive reals such that x3+7x2+24x+18=(x+a)(x+b+ci)(x+bci),\begin{aligned} & x^3+7x^2+24x+18 \\ &= (x+a)(x+b+ci)(x+b-ci), \end{aligned} where ii is the imaginary number that satisfies i2=1.i^2=-1. What is the value of a+b+c?a+b+c?

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