#### Answer

$x=\left\{ -\dfrac{3}{2},7 \right\}$

#### Work Step by Step

x^{y}$\bf{\text{Solution Outline:}}$
To solve the given equation, $
-2x^2+11x=-21
,$ express first in the form $ax^2+bx+c=0.$ Then factor the left side. Equate each factor to zero (Zero Product Property). Finally, use the properties of equality to isolate the variable in each equation.
$\bf{\text{Solution Details:}}$
In the form $ax^2+bx+c=0,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
-2x^2+11x+21=0
\\\\
-1(-2x^2+11x+21)=-1(0)
\\\\
2x^2-11x-21=0
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the factored form of equation above is
\begin{array}{l}\require{cancel}
(2x+3)(x-7)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
2x+3=0
\\\\\text{OR}\\\\
x-7=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x+3=0
\\\\
2x=-3
\\\\
x=-\dfrac{3}{2}
\\\\\text{OR}\\\\
x-7=0
\\\\
x=7
.\end{array}
Hence, the solutions are $
x=\left\{ -\dfrac{3}{2},7 \right\}
.$