Answer
$t=\dfrac{3}{2}$
Work Step by Step
Using factoring of trinomials, the given equation, $
4t^2-12t+9=0
,$is equivalent to
\begin{align*}
(2t-3)(2t-3)&=0
\\
(2t-3)^2&=0
.\end{align*}
Taking the square root of both sides (Square Root Property) and solving for the variable, the equation above is equivalent to
\begin{align*}
2t-3&=\pm\sqrt{0}
\\
2t-3&=0
\\
2t&=3
\\
t&=\dfrac{3}{2}
.\end{align*}
Hence, the solution of the equation $
4t^2-12t+9=0
$ is $t=\dfrac{3}{2}$.
