Goal Seek for achieving two simultaneous goals

I have a format for bifurcating sales amount among different tax slabs (2.5%, 12.5%, 18% & 28%)

Net values in column D represent the basic value, VAT amount values in column E are subsequent VAT values (Net X Rate)

I have the following values that are known:
Total Net Amount (Cell D1)
Total Vat Amount (Cell E1)

The Result expected:
Sum of Current Net Values = Cell D2
Sum of VAT AMount Values = Cell E2

Condition: The amounts within D6 to D9 need to be adjusted in such a way that subsequent VAT Amount total is also equal to the total of VAT known (E2)

I have used the macro for Goal seek but it allows to change only 1 set of values. There are multiple such calculations required on different occassions.

Could you help me find a better way to do this?

Is the problem solvable? Why is the VAT in E6 calculated differently from the VATs in E7:E9? Are you required to use Goal Seek, or will a different approach be allowed.

I like to solve problems like this mathematically/algebraically before trying to program the solution. At first glance, it looks like a "system of equations" kind of problem where you have 2 equations in 4 unknowns (so there are likely many possible solutions if it can be solved). Solving as a system of equations should allow you to completely bypass a numeric "goal seek" algorithm and program in a direct solution.

The first question might be to determine if a solution is possible. In this case, assuming that All Net values must be greater than or equal to 0 (not negative Nets), the values in D3 and E3 suggest that you need an average rate of about 41%, but the highest Rate in column C is 28%. Assuming all Nets must be greater than 0, then the example in the attached seems unsolvable.

Once determined that the problem can be solved, I can choose any reasonable value for any two of the values in D6:D9 (the average Rate determined by dividing E3 by D3 should be useful for this), then solve for the other two values as a system of 2 equations in 2 unknowns.

What do you think? Is that too much algebra to get simpler programming, or do you want to continue to pursue a "goal seek" type algorithm solution?

Remembering the algebra to solving these begins with this series of algebra lessons: https://www.purplemath.com/modules/systlin1.htm Then ends here, https://www.excel-easy.com/examples/...equations.html where we take everything learned about solving systems of equations and reduce it to a few simple matrix operations that are preprogrammed into the Excel functions MMULT() and MINVERSE().

Nettotal=SUM(NETs)=Net1+Net4+SUM(otherNETs)
VATtotal=SUM(VATs)=SUMPRODUCT(NETs,RATEs)=Net1*Rate1+Net4*Rate4+SUMPRODUCT(otherNets,otherRates)
Move all of the "known" terms to one side:
NETtotal-SUM(otherNETs)=NET1+NET4
VATtotal-SUMPRODUCT(otherNETs,otherRates)=NET1*Rate1+NET4*Rate4
Put into the terms of Excel Easy's matrix solution A={1,1;Rate1,Rate4}, X={NET1;NET4}, B={NETtotal-SUM(otherNETs);VATtotal-SUMPRODUCT(otherNETs,otherRATEs)}

Now I can build these matrices in the spreadsheet and solve the system of equations for whatever values I want to enter in NET3 (D7) and NET2(D6).

For matrix A, Enter 1 in B13 and C13 and enter =C6 in B14 and =C9 in C14.
For matrix B, enter =D3-SUM(D7:D8) into E13 and enter =E3-SUM(E7:E8) into E14
The inverse of A is =MINVERSE(B13:C14) array entered into G13:H14
The X matrix (and the solution to the problem) is =MMULT(G13:H14,E13:E14) array entered into J13:J14

To check the solution, I can enter =J13 into D6 and =J14 into D9 and see that the solution works.

The reason I asked about whether or not the given example was solvable is that the average Rate for NETtotal of 6100 and VATtotal of 2500 is 2500/6100=41%. The highest rate in C6:C9 is 28%. From this observation, I know that I cannot get an average Rate of 41% from rates of 2.5 to 28% unless at least one of NETs is less than 0. If you don't care that one or more NETs can be negative, then the algebra/programming don't care. If you need a programming step to test for averageRate between 2.5 and 28% in order to flag problems where the solution must include one negative number, then you can include that extra programming step. If having all NETs be greater than 0, it may also be valuable to calculate some limits on D7 and D8 so that you know what values are allowed in these cells so that D6 and D9 don't end up being negative.

For generations, one of the biggest challenges in math education has been to help students see how what they learn in math classes applies to other fields -- including commerce. I am not enough of a math educator to bridge that gap for you, but I might suggest that, if you can figure out how to apply what you have learned in math classes to your commerce coursework, you will find that your commerce coursework will be easier.

I am attaching a spreadsheet with the solution I outlined in post #4. Perhaps it will help you understand what I proposed in post #4, or perhaps it will confuse you even more. Review the spreadsheet and review what I wrote in post #4 and see if it helps you understand how we are applying math to the commerce problem.