Answer
$x=2$,
$x=-3,-1,2$
Work Step by Step
Step 1. With the given graph, we can determine a solution of the equation as $x=2$.
Step 2. The coefficients of the dividend $f(x)=x^3+2x^2-5x-6$ can be identified in order as $\{1,2,-5,-6\}$ and the divisor is $x-2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(x^2+4x+3)(x-2)=(x+1)(x+3)(x-2)$; thus we can find the zeros of $f(x)$ as $x=-3,-1,2$
