Answer
The solution is $p=15$.
Work Step by Step
The given equation is
$\Rightarrow 7+3\sqrt{3p-9}=25$
Subtract $7$ from each side.
$\Rightarrow 7+3\sqrt{3p-9}-7=25-7$
Simplify.
$\Rightarrow 3\sqrt{3p-9}=18$
Divide each side by $3$.
$\Rightarrow \sqrt{3p-9}=6$
Square each side of the equation.
$\Rightarrow (\sqrt{3p-9})^2=(6)^2$
Simplify.
$\Rightarrow 3p-9=36$
Add $9$ to each side.
$\Rightarrow 3p-9+9=36+9$
Simplify.
$\Rightarrow 3p=45$
Divide each side by $3$.
$\Rightarrow p=15$
Check $p=15$.
$\Rightarrow 7+3\sqrt{3p-9}=25$
$\Rightarrow 7+3\sqrt{3(15)-9}=25$
$\Rightarrow 7+3\sqrt{45-9}=25$
$\Rightarrow 7+3\sqrt{36}=25$
$\Rightarrow 7+3(6)=25$
$\Rightarrow 7+18=25$
$\Rightarrow 25=25$
True.
Hence, the solution is $p=15$.
