How to find the interest rate?

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Lets say we have this following scenario:

1000000 = 1000 * (1/r) * [1-(1/(1+r)^43)],

where PV=1000000, n=43, C=1000, r=?

We have to find "r", so how do we manually go about finding "r"? I know "r" can be found by using a financial calculator but I am interested in knowing how it can be calculated manually as such stuff is not taught our class.