Find the two numbers

One number is 2 more than 3 times another. Their product is 16. Find the numbers.

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x = one number
3x + 2 = other number  {one number is 2 more than 3 times the other}

x(3x + 2) = 16   {their product is 16}
3x² + 2x = 16   {used distributive property}
3x² + 2x - 16 = 0   {subtracted 16 from each side}
(3x + 8)(x - 2) = 0   {factored into two binomials}
3x + 8 = 0  or  x - 2 = 0  {set each factor equal to zero}
x = -8/3  or  x = 2  {solved each equation}
3x + 2 = -6  or  3x + 2 = 8  {substituted -8/3 and 2, in for x, into 3x + 2}

The two sets of numbers could be -8/3 and -6, or  2 and 8.

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