Question 94156
Let x = the first positive even integer, then x+2  is the next consecutive positive integer.  The product of these two = 288.  So we can set up the equation to solve for x:
{{{x(x+2) = 288}}} Apply the distributive property to the left side.
{{{x^2+2x = 288}}} Subtract 288 from both sides.
{{{x^2+ 2x-288 = 0}}} Factor the left side.
{{{(x-16)(x+18) = 0}}} Apply the zero products principle.
{{{x-16 = 0}}} or {{{x+18 = 0}}} so...
x = 16 or x = -18 but you want the positive integer only, so...
x = 16 this is the first positive even integer.
x+2 = 18  This is the next consecutive positive even integer.

Check:

(16)(18) = 288