Answer
$[-4,3]$
Work Step by Step
$(x-3)(x+4)\leq0$
$(x-3)(x+4) =0$ Solve as an equation.
$x=3$
$x=-4$
Plot these numbers on a number line,split them into intervals, take one test point from each interval, and check them to see if they are true. If they are true, then it is a solution.
In this case, it is
$[-4,3]$