Question

T²= 4π² (M+m) ÷ ug

Answer 1

Starting with ...

$T^2=\dfrac{4\pi^2(M+m)}{ug}$

1) Multiply by the inverse of the coefficient multiplying the sum with M, then subtract m.

$\dfrac{T^2ug}{4\pi^2}=M+m\\\\M=\dfrac{T^2ug}{4\pi^2}-m$

2) Multiply by g/T²

$g=\dfrac{4\pi^2(M+m)}{T^2u}$