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\sqrt{3n+8}-5-\left(-5\right)=-\left(-5\right)
Add 5 to both sides of the equation.
\sqrt{3n+8}=-\left(-5\right)
Subtracting -5 from itself leaves 0.
\sqrt{3n+8}=5
Subtract -5 from 0.
3n+8=25
Square both sides of the equation.
3n+8-8=25-8
Subtract 8 from both sides of the equation.
3n=25-8
Subtracting 8 from itself leaves 0.
3n=17
Subtract 8 from 25.
\frac{3n}{3}=\frac{17}{3}
Divide both sides by 3.
n=\frac{17}{3}
Dividing by 3 undoes the multiplication by 3.