Factorise and solve:
x^2 + 6x - 72 = 0
$\displaystyle x^2+6x-72=0$
We try find the factos adding to 6
$\displaystyle 1(-72)=-72$ $\displaystyle -71$
$\displaystyle 2(-36)=-72$ $\displaystyle -34$
$\displaystyle 3(-24)=-72$ $\displaystyle -21$
$\displaystyle 4(-18)=-72$ $\displaystyle -14$
$\displaystyle 6(-12)=-72$ $\displaystyle -6$
$\displaystyle 12(-6)=-72$ $\displaystyle 6$
Now we have to re-write our equation
$\displaystyle x^2+12x-6x-72=0$
$\displaystyle x(x+12)-6(x+12)=0$
$\displaystyle (x-6)(x+12)=0$
Then:
$\displaystyle x-6=0$
$\displaystyle x=6$
or
$\displaystyle x+12=0$
$\displaystyle x=-12$