#### Answer

$x=\left\{ -2,2 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Express the given equation, $
-2x^2+8=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}
-2(x^2-4)=0
\\\\
-2(x+2)(x-2)=0
\\\\
\dfrac{-2(x+2)(x-2)}{-2}=\dfrac{0}{-2}
\\\\
(x+2)(x-2)=0
.\end{array}
Equating each factor to zero (Zero-Factor Property), then
\begin{array}{l}\require{cancel}
x+2=0
\text{ OR }
x-2=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
x+2=0
\\\\
x=-2
\\\\\text{ OR }\\\\
x-2=0
\\\\
x=2
.\end{array}
Hence, the solutions are $
x=\left\{ -2,2 \right\}
.$
$\bf{\text{Supplementary Solution/s:}}$
Factoring the negative $GCF=
-2
,$ the expression, $
-2x^2+8
,$ above is equivalent to
\begin{array}{l}\require{cancel}
-2 \left( \dfrac{-2x^2}{-2}+\dfrac{8}{-2} \right)
\\\\=
-2 \left( x^2-4 \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}
-2 \left( x+2 \right)\left( x-2 \right)
.\end{array}