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In page Equation:

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Two equations or two systems of equations are equivalent, if they have the same set of solutions. The following operations transform an equation or a system of equations into an equivalent one – provided that the operations are meaningful for the expressions they are applied to:

  • Adding or subtracting the same quantity to both sides of an equation.[citation needed] This shows that every equation is equivalent to an equation in which the right-hand side is zero.
  • Multiplying or dividing both sides of an equation by a non-zero quantity.[citation needed]
  • Applying an identity to transform one side of the equation. For example, expanding a product or factoring a sum.