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That really depends on the equation. In the simplest cases, you need to isolate the variable on one side - eliminate anything other than the variable, by doing the same operation on both sides. For example, if you have an "x + 3" on one side, subtract 3 on both sides, to remove the "3" from the left side.
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How do you solve these equations?
Tell me the equations first.
How do you solve multivariable equations?
You need as many equations as you have variables.
How do you solve 3 dimensional equations?
You can solve the system of equations with three variables using the substitute method, or using matrix operations.
Why do you need to be able to solve equations?
If you don't learn to solve equations then guess and check is the only way to arrive at new information.
Solve linear equations with complex coefficients on both sides?
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
