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The multivariable solver integrated into LibreOffice is activated by the Menu Tools ▸ Solver.

The solver engine by default supports only linear equations, but the NLPSolver extension allows you to handle non-linear problems. You will find a full explanation of its functioning on [1].

Yous can also use the tool Goal seek :

  1. Set out the equations for your problem, with a cell to contain the initial value that is to be determined, and another containing the formula whose result needs to reach a certain value (the target value).
  2. Go to Tools ▸ Goal Seek.
  3. In Formula Cell, indicate the coordinates of the cell containing the formula which needs to attain the target value.
  4. In Target Value, indicate the value that should be reached in the preceding case.
  5. In Variable Cell, indicate the coordinates of the cell whose value is unknown and will be modified.
  6. Click OK.