(3n^2+1)+(8n^2-1)=0

Solution for (3n^2+1)+(8n^2-1)=0 equation:

Simplifying
(3n2 + 1) + (8n2 + -1) = 0

Reorder the terms:
(1 + 3n2) + (8n2 + -1) = 0

Remove parenthesis around (1 + 3n2)
1 + 3n2 + (8n2 + -1) = 0

Reorder the terms:
1 + 3n2 + (-1 + 8n2) = 0

Remove parenthesis around (-1 + 8n2)
1 + 3n2 + -1 + 8n2 = 0

Reorder the terms:
1 + -1 + 3n2 + 8n2 = 0

Combine like terms: 1 + -1 = 0
0 + 3n2 + 8n2 = 0
3n2 + 8n2 = 0

Combine like terms: 3n2 + 8n2 = 11n2
11n2 = 0

Solving
11n2 = 0

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Divide each side by '11'.
n2 = 0

Simplifying
n2 = 0

Take the square root of each side:
n = {0}