Answer
$x=-2,8$
Work Step by Step
$f(x)=x^2-6x-16$
Since we are solving for all the real values of $x$ when $f(x) = 0$, set the function $f(x)=x^2-6x-16$ equal to zero and we get the following equation:
$x^2-6x-16=0$
Now factor the left side of the equation by finding two numbers that multiply to get -16 and add to get -6. These two numbers are 2 and -8. So the factored left side looks as follows:
$(x+2)(x-8)=0$
Next, you can see that the above equation holds true when $x+2=0$ or $x-8=0$. Solve each of those two equations individually.
$x+2=0$
Subtract 2 from both sides.
$x+2-2=0-2$
$x=-2$
Now for the other equation:
$x-8=0$
Add 8 to both sides.
$x-8+8=0+8$
$x=8$
So, the final solution is $x=-2,8$
