Answer
$x=\dfrac{1}{2}$
Work Step by Step
Dividing both sides by the $GCF=3,$ the given expression, $
12x^2-12x+3=0
,$ is equivalent to
\begin{align*}
\dfrac{12x^2-12x+3}{3}&=\dfrac{0}{3}
\\\\
4x^2-4x+1&=0
.\end{align*}
Using the square of a binomial which is given by $(a+b)^2=(a)^2+2(a\cdot b)+(b)^2$ or by $(a-b)^2=(a)^2-2(a\cdot b)+(b)^2,$ the expression above is equivalent to
\begin{align*}
(2x)^2-2(2x\cdot1)+(1)^2&=0
\\
(2x-1)^2&=0
.\end{align*}
Taking the square root of both sides (Square Root Principle), the expression above is equivalent to
\begin{align*}
2x-1&=\pm\sqrt{0}
\\
2x-1&=0
\\
2x-1+1&=0+1
\\
2x&=1
\\\\
\dfrac{2x}{2}&=\dfrac{1}{2}
\\\\
x&=\dfrac{1}{2}
.\end{align*}
Hence, the solution is $
x=\dfrac{1}{2}
$.
