78n^2=-2-80n

Solution for 78n^2=-2-80n equation:

Simplifying
78n2 = -2 + -80n

Solving
78n2 = -2 + -80n

Solving for variable 'n'.

Reorder the terms:
2 + 80n + 78n2 = -2 + -80n + 2 + 80n

Reorder the terms:
2 + 80n + 78n2 = -2 + 2 + -80n + 80n

Combine like terms: -2 + 2 = 0
2 + 80n + 78n2 = 0 + -80n + 80n
2 + 80n + 78n2 = -80n + 80n

Combine like terms: -80n + 80n = 0
2 + 80n + 78n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 40n + 39n2) = 0

Factor a trinomial.
2((1 + n)(1 + 39n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Subproblem 2
Set the factor '(1 + 39n)' equal to zero and attempt to solve:

Simplifying
1 + 39n = 0

Solving
1 + 39n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 39n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 39n = 0 + -1
39n = 0 + -1

Combine like terms: 0 + -1 = -1
39n = -1

Divide each side by '39'.
n = -0.02564102564

Simplifying
n = -0.02564102564
Solution
n = {-1, -0.02564102564}