Answer
$\left\{-\dfrac{2}{3},2\right\}$
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
-3x^2+4x=-4
,$ is equivalent to
\begin{align*}
-3x^2+4x+4&=0
\\
-1(-3x^2+4x+4)&=(0)(-1)
\\
3x^2-4x-4&=0
.\end{align*}
Using factoring of trinomials, the equation above is equivalent to
\begin{align*}
(x-2)(3x+2)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l|r}
x-2=0 & 3x+2=0
\\
x=2 & 3x=-2
\\\\
& x=-\dfrac{2}{3}
.\end{array}
Hence, the solution set of the equation $
5x^6+2x^3-7=0
$ is $\left\{-\dfrac{2}{3},2\right\}$.
