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what is 3x^2+2x-16=0

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1 Answer

     3x2 + 2x - 16 = 0

Since the equation is set equal to 0, we know that we are looking to solve for the roots (or real zeros) of the equation by finding what x is when the equation is equal to 0.

First, we factor the left hand side of the equation:

      3x2 + 2x - 16  =  0

     (3x + 8)(x - 2)  =  0

By the zero product property, since   (3x + 8)(x - 2) = 0 , then either   (3x + 8) = 0  or  (x - 2) = 0.

That is, either:      3x + 8 = 0                        or                      x - 2 = 0

                           3x + 8 - 8  = 0 - 8                                      x - 2 + 2  = 0 + 2

                           3x = -8                                                      x = 2

                          (3x) / 3 = (-8) / 3

                           x = -8/3 

Thus,    3x2 + 2x - 16 = 0   when   x = -8/3    or when    x = 2