<PRE><B>Question 1147129</B>
&lt;br&gt;
Let the two even integers be x and x+2.  Then their product, increased by the smaller integer, is&lt;br&gt;
x(x+2)+x = x^2+2x+x = x^2+3x&lt;br&gt;
You want that expression to equal 180:&lt;br&gt;
{{{x^2+3x = 180}}}
{{{x^2+3x-180 = 0}}}&lt;br&gt;
Solve by factoring.  (I leave that to you....)&lt;br&gt;
If a formal algebraic solution is not required, the answer can be found more quickly using trial and error.&lt;br&gt;
{{{x^2+3x = 180}}}
{{{x(x+3) = 180}}}&lt;br&gt;
Look for two integers whose difference is 3 and whose product is 180, with the restriction that the smaller number is even.  The two numbers are 12 and 15.&lt;br&gt;
So the smaller of the two even integers is 12 and the other is 14.&lt;br&gt;
Note that, algebraically, the equation has two solutions, the other of which is -15.  However, since the problem is about consecutive even integers, that solution has to be rejected.</PRE>