Answer
$x=3$ and $x=-2$
Work Step by Step
$\log_{6}(x^{2}-x)=1$
Rewrite in exponential form:
$6^{1}=x^{2}-x$
$x^{2}-x=6$
Take the $6$ to the left side of the equation:
$x^{2}-x-6=0$
Solve this equation by factoring:
$(x-3)(x+2)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-3=0$
$x=3$
$x+2=0$
$x=-2$
The initial equation is not undefined for either of the solutions, so our answer is:
$x=3$ and $x=-2$