College Algebra, Chapter 5, 5.4, Section 5.4, Problem 34

Solve the equation $x^2 10^x - x 10^x = 2(10^x)$

$
\begin{equation}
\begin{aligned}
x^2 10^x - x 10^x &= 2(10^x)\\
\\
10^x(x^2-x) &=2 (10^x) && \text{Factor out } 10^x\\
\\
\frac{\cancel{10^x}(x^2-x)}{\cancel{10^x}} &= \frac{2(\cancel{10^x})}{\cancel{10^x}} && \text{Divide both sides by } 10^x\\
\\
x^2 - x &= 2&& \text{Subtract 2}\\
\\
x^2 - x - 2 &= 0 && \text{Factor using trial and error }\\
\\
(x-2)(x+1) &= 0
\end{aligned}
\end{equation}
$

Solve for $x$

$
\begin{equation}
\begin{aligned}
x-2 &= 0
&&&
x +1 &= 0\\
\\
x &= 2
&&\text{and}&
x &= -1
\end{aligned}
\end{equation}
$