The Power of Absolute - 2

The above equation can be written as: $25+3(5*3)^{\left | x \right |}=5^{\left | x \right |}+25(3^{\left | x \right |+1})$

$\Rightarrow 25+5^{\left | x \right |}(3^{\left | x \right |+1})=5^{\left | x \right |}+25(3^{\left | x \right |+1})$

$\Rightarrow 5^{\left | x \right |}(3^{\left | x \right |+1}-1)=25(3^{\left | x \right |+1}-1)$

$\Rightarrow (3^{\left | x \right |+1}-1)(5^{\left | x \right |}-25)=0$

Hence, either $3^{\left | x \right |+1}-1=0$ or $5^{\left | x \right |}-25=0$

$\Rightarrow 3^{\left | x \right |+1}=1$ or $5^{\left | x \right |}=25$

$\Rightarrow \left | x \right |+1=0$ or $\left | x \right |=2$

$\Rightarrow \left | x \right |=-1$ (This is not possible) or $x=\pm 2$

Hence, $x=\pm 2$ are the only possible values that x can take.

Therefore, product of all values of x satisfying the given equation is: $2*(-2)=\boxed{-4}$