Answer
$(x+12)(x-6)$
Work Step by Step
To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$.
In the case of $x^2+6x-72$, we are looking for two numbers whose product is $-72$ and whose sum is $6$. The numbers $12$ and $-6$ meet these criteria, because $$12\times-6=-72\;\text{and}\;12+(-6)=6$$When we insert these numbers into the blanks, we arrive at the factors $(x+12)(x-6)$.
