Collect coefficients from a complex equation

I'm new to wolfram and I was solving an optimization question in wolfram. For that I need to calculate the objective function.

From my calculations I got a equation (with complex numbers) as follows:

0. + 3.35/((23.4256 + (0. + 3.35/\[Alpha])^2) \[Alpha]) +
I (-(4.84/(23.4256 + (0. + 3.35/\[Alpha])^2)) + (
3 \[Pi] \[Alpha]^2)/500 - 108./(
11664. + 3.0976/(\[Alpha] - \[Beta])^2)) + 1.76/((11664. +
3.0976`/(\[Alpha] - \[Beta])^2) (\[Alpha] - \[Beta])) Now I need to collect the real part from the above equation which is easy, but after that I need to equate the real part to zero and rearrange it in the following form

$$A_5 \alpha^5 + A_4 \alpha^4 + A_3 \alpha^3 + A_2 \alpha^2 + A_1 \alpha + A_0 = 0$$

What should I do ? Assuming $\alpha$ and $\beta$ are real numbers.

• Numerator: Take the numerator of said fraction. This is equivalent to multiplying both sides of the equations with the denominator: $\frac ab=0\Rightarrow a=b\cdot 0\Rightarrow a=0$