Answer
$x=\left\{ -3,3 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Express the given equation, $
-3x^2+27=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}
-3(x^2-9)=0
\\\\
-3(x+3)(x-3)=0
\\\\
\dfrac{-3(x+3)(x-3)}{-3}=\dfrac{0}{-3}
\\\\
(x+3)(x-3)=0
.\end{array}
Equating each factor to zero (Zero-Factor Property), then
\begin{array}{l}\require{cancel}
x+3=0
\text{ OR }
x-3=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
x+3=0
\\\\
x=-3
\\\\\text{ OR }\\\\
x-3=0
\\\\
x=3
.\end{array}
Hence, the solutions are $
x=\left\{ -3,3 \right\}
.$
$\bf{\text{Supplementary Solution/s:}}$
Factoring the negative $GCF=
-3
,$ the expression, $
-3x^2+27
,$ above is equivalent to
\begin{array}{l}\require{cancel}
-3 \left( \dfrac{-3x^2}{-3}+\dfrac{27}{-3} \right)
\\\\=
-3 \left( x^2-9 \right)
.\end{array}
Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-3 \left( x+3 \right) \left( x-3 \right)
.\end{array}
