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How to Solve Equations With Parentheses

Mathematical equations are sometimes written with parentheses. Sometimes the parentheses are just to make it easier to read the equation, but usually they are placed so as to alter the usual order of operations. In an equation without parentheses, you first take exponents, then divide and multiply, then add and subtract. For instance, 3+2*4+3^2 = 3+2*4+9 = 3+8+9 = 20.

The order of operations is the opposite of the order in which you learned the operations in school, where first you learned to add and subtract, then to multiply and divide and then to take powers.

Instructions

- 1
  Expand the innermost set of parentheses, using the usual order of operations. For example, suppose the equation is
  
  4*(3*(8-5)^2 +2). The inner set of parentheses is (8-5) so evaluate that and get
  
  4*(3*3^2 + 2).
- 2
  Expand the next set of parentheses, again following the usual order of operations. The next set of parentheses is (3*3^2+2). First take powers, getting 4*(3*9+2) then multiply getting 4*(27+2). Then add, getting 4*29.
- 3
  Repeat Step 2 as necessary. In the example, there are no more parentheses.
- 4
  Evaluate the remaining expression, again following the usual order of operations. In the example 4*29 = 116. Note that without parentheses 4*3*8-5^2 +2 = 4*3*7-25+2 = 12*7-25+2 = 84-25+2 = 61, and you can see that parentheses make a big difference.

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