(3n^2+1)-(8n^2-16)=

Solution for (3n^2+1)-(8n^2-16)= equation:

Simplifying
(3n2 + 1) + -1(8n2 + -16) = 0

Reorder the terms:
(1 + 3n2) + -1(8n2 + -16) = 0

Remove parenthesis around (1 + 3n2)
1 + 3n2 + -1(8n2 + -16) = 0

Reorder the terms:
1 + 3n2 + -1(-16 + 8n2) = 0
1 + 3n2 + (-16 * -1 + 8n2 * -1) = 0
1 + 3n2 + (16 + -8n2) = 0

Reorder the terms:
1 + 16 + 3n2 + -8n2 = 0

Combine like terms: 1 + 16 = 17
17 + 3n2 + -8n2 = 0

Combine like terms: 3n2 + -8n2 = -5n2
17 + -5n2 = 0

Solving
17 + -5n2 = 0

Solving for variable 'n'.

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

Add '-17' to each side of the equation.
17 + -17 + -5n2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -5n2 = 0 + -17
-5n2 = 0 + -17

Combine like terms: 0 + -17 = -17
-5n2 = -17

Divide each side by '-5'.
n2 = 3.4

Simplifying
n2 = 3.4

Take the square root of each side:
n = {-1.843908891, 1.843908891}