Strategy for Solving Polynomial Equations

Step 1.  Simplify both expressions as much as possible.

Step 2.  Get all terms on one side of the equation so that it is equal to zero.

Step 3.  Simplify both expressions as much as possible.

Step 4.  Factor the polynomial as completely as possible.  (Note:  When this step is completed, one should have only linear factors and irreducible quadratic factors!)

Step 5.  Because a product can be zero if and only if one of the factors is zero, set each factor equal to zero.

Step 6.  Solve the resulting linear and quadratic equations.  (Note:  Since the only quadratic equations should result from irreducible quadratic polynomials, it will be necessary to either "complete the square" or use the quadratic formula to solve these equations.)

At this point, you are finished.