Answer
$x_{1}=0$ and $x_{2}=1$
Work Step by Step
$(x+6)(x-6)=(2x-9)(x+4)$
$x(x-6)+6(x-6)=2x(x+4)-9(x+4)$
$x^2-6x+6x-36=2x^2+8x-9x-36$
$x^2-36=2x^2-x-36$
$2x^2-x^2-x-36+36=0$
$x^2-x=0$
$x(x-1)=0$
Therefore the solutions are $x_{1}=0$ and $x_{2}=1$