Answer
$x=2$ and $x=-1$
Work Step by Step
$x^{2}10^{x}-x10^{x}=2(10^{x})$
Take $2(10^{x})$ to the left side of the equation:
$x^{2}10^{x}-x10^{x}-2(10^{x})=0$
Take out common factor $10^{x}$:
$10^{x}(x^{2}-x-2)=0$
Factor $x^{2}-x-2$:
$10^{x}(x-2)(x+1)=0$
Set all three factors equal to $0$ and solve each individual equation:
$10^{x}=0$
Since no value of $x$ makes this first equation true, it has no solution. Move on to the second one:
$x-2=0$
Solve for $x$:
$x=2$
Move on to the third one:
$x+1=0$
Solve for $x$:
$x=-1$
Our two solutions are:
$x=2$ and $x=-1$
