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 $x$

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