#### Answer

$x=\left\{ 0,9 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Express the given equation, $
3x^2-27x=0
,$ in factored form. Then, use the Zero-Factor Property by equating each factor to zero. Finally, solve each equation.
$\bf{\text{Solution Details:}}$
The factored form of the equation above is
\begin{array}{l}\require{cancel}
3x(x-9)=0
.\end{array}
Equating each factor to zero (Zero-Factor Property), then
\begin{array}{l}\require{cancel}
3x=0
\text{ OR }
x-9=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
3x=0
\\\\
x=\dfrac{0}{3}
\\\\
x=0
\\\\\text{ OR }\\\\
x-9=0
\\\\
x=9
.\end{array}
Hence, the solutions are $
x=\left\{ 0,9 \right\}
.$
$\bf{\text{Supplementary Solution/s:}}$
In the expression $
3x^2-27x
,$ the $GCF$ of the constants of the terms $\{
3,-27
\}$ is $
3
.$ The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
x^2,x
\}$ is $
x
.$ Hence, the entire expression has $GCF=
3x
.$
Factoring the $GCF=
3x
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3x \left( \dfrac{3x^2}{3x}-\dfrac{27x}{3x} \right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
3x \left( x^{2-1}-9x^{1-1} \right)
\\\\=
3x \left( x^{1}-9x^{0} \right)
\\\\=
3x \left( x-9(1) \right)
\\\\=
3x \left( x-9 \right)
.\end{array}