7n^2+30=-47n

Solution for 7n^2+30=-47n equation:

Simplifying
7n2 + 30 = -47n

Reorder the terms:
30 + 7n2 = -47n

Solving
30 + 7n2 = -47n

Solving for variable 'n'.

Reorder the terms:
30 + 47n + 7n2 = -47n + 47n

Combine like terms: -47n + 47n = 0
30 + 47n + 7n2 = 0

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

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 + 7n)' equal to zero and attempt to solve:

Simplifying
5 + 7n = 0

Solving
5 + 7n = 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 + 7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7n = 0 + -5
7n = 0 + -5

Combine like terms: 0 + -5 = -5
7n = -5

Divide each side by '7'.
n = -0.7142857143

Simplifying
n = -0.7142857143
Solution
n = {-6, -0.7142857143}