The product of two consecutive even integers is 288 find the integers.

Using algebra

n and n+2 are the integers

n * (n+2) = 288

n^2+2n=288

n^2+2n-288=0

288=2*2*2*2*2*3*3 = (2*2*2*2) * (2*3*3) = 16*18 and 18-16=2

factor (n+18) (n-16) = 0

n+18=0

n=-18

n+2=-16

this is one solution

n-16=0

n=16

n+2=18

this is another solution

as you can see, it's just a matter of factoring 288using arithmetic ... √288=16.97≈1716 and 18 are the integers (as well as - 16 and - 18)