#### Answer

$\color{blue}{\left\{-2.5, 2.5\right\}}$

#### Work Step by Step

Subtract $5$ to both sides:
$4x^2-20-5=5-5
\\4x^2-25=0
\\(2x)^2-5^2=0$
Factor the binomial using the formula $a^2-b^2=(a-b)(a+b)$, where $a=2x$ and $b=5$ to obtain:
$(2x-5)(2x+5)=0$
RECALL:
The Zero-Factor Property states that if $ab=0$, then $a=0$ or $b=0$, or both are zero.
Use the Zero-Factor Property by equating each factor to zero to obtain:
$2x-5=0$ or $2x+5=0$
Solve each equation to obtain:
$2x-5=0
\\2x=5
\\\frac{2x}{2}=\frac{5}{2}
\\x=2.5$
or
$2x+5=0
\\2x+5-5=0-5
\\2x=-5
\\\frac{2x}{2}=\frac{-5}{2}
\\x=-2.5$
Therefore, the solution set is $\color{blue}{\left\{-2.5, 2.5\right\}}$.