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SolveEquation
 SolveEquation[eqns, vars] attempts to solve an equation or set of equations for the variables vars.
Equations are given in the form lhs == rhs.
Simultaneous equations can be combined either in a list or with &&.
A single variable or a list of variables can be specified.
SolveEquation[eqns] tries to solve for all variables in eqns.
Example: SolveEquation[3 x + 9 == 0, x]  
When there are several solutions, SolveEquation gives a list of them.
When a particular root has multiplicity greater than one, SolveEquation gives several copies of the corresponding solution.
SolveEquation deals primarily with linear and polynomial equations.
SolveEquation gives generic solutions only. It discards solutions that are valid only when the parameters satisfy special conditions.
SolveEquation gives {} if there are no possible solutions to the equations.
See also: LocateRoot, SolveODE.
Examples
Using InstantCalculators
Here are the InstantCalculators for the SolveEquation function. Enter the parameters for your calculation and click Calculate to see the result.
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Entering Commands Directly
You can paste a template for this command via the Text Input button on the SolveEquation Function Controller.
Polynomial equations in one variable
These are standard formulas for the solutions of normalized quadratic and cubic equations.
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Here are two simple equations of higher degree with solutions in terms of powers. They can be rewritten in terms of trigonometric functions that sometimes automatically reduce to radicals.
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Polynomial equations in more than one variable
Here we solve for x and y.
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Clear the variable definition.
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Here we solve two simultaneous algebraic equations.
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Here are three simultaneous algebraic equations; y and z must be paired up correctly with x.
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Here SolveEquation returns an empty list, indicating no solution. Every potential solution forces an equation in the parameter z alone, so there are no generic solutions.
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We can get solutions by solving for z as well as x and y.
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Equations involving trigonometric or hyperbolic functions, or their inverses
This is an example using the trigonometric function cosine.
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Equations involving exponentials and logarithms
This uses the ordinary mathematical notation for Exp.
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