7n^2+210=-77n

Solution for 7n^2+210=-77n equation:

Simplifying
7n2 + 210 = -77n

Reorder the terms:
210 + 7n2 = -77n

Solving
210 + 7n2 = -77n

Solving for variable 'n'.

Reorder the terms:
210 + 77n + 7n2 = -77n + 77n

Combine like terms: -77n + 77n = 0
210 + 77n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(30 + 11n + n2) = 0

Factor a trinomial.
7((6 + n)(5 + n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {-6, -5}