#### Answer

$x=\left\{ \dfrac{1}{6},\dfrac{1}{2} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
12x^2=8x-1
,$ express first in the form $ax^2+bx+c=0.$ Then factor the left side. Equate each factor to zero (Zero Product Property). Finally, use the properties of equality to isolate the variable in each equation.
$\bf{\text{Solution Details:}}$
In the form $ax^2+bx+c=0,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
12x^2-8x+1=0
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the factored form of equation above is
\begin{array}{l}\require{cancel}
(2x-1)(6x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
2x-1=0
\\\\\text{OR}\\\\
6x-1=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x-1=0
\\\\
2x=1
\\\\
x=\dfrac{1}{2}
\\\\\text{OR}\\\\
6x-1=0
\\\\
6x=1
\\\\
x=\dfrac{1}{6}
.\end{array}
Hence, the solutions are $
x=\left\{ \dfrac{1}{6},\dfrac{1}{2} \right\}
.$