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3x^{2} + 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:

3x^{2} + 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, 3x^{2} + 2x - 16 = 0 when x = -8/3 or when x = 2