Answer:
x = -3, 9
Explanation:
First, let us divide both sides of the equation by 10^x; this gives,
[tex]\frac{x^210^x-6x\times10^x}{10^x}=\frac{27\times10^x}{10^x}[/tex][tex]\Rightarrow x^2-6x=27[/tex]
subtracting 27 from both sides gives
[tex]x^2-6x-27=0[/tex]
The left-hand side can be factored as
[tex](x-9)(x+3)=0[/tex]
which gives us two further equations
[tex]\begin{gathered} x-9=0 \\ \boxed{x=9.} \end{gathered}[/tex][tex]\begin{gathered} x+3=0 \\ \Rightarrow\boxed{x=-3.} \end{gathered}[/tex]
Hence, the two solutions we get are x = 9 and x = -3.
