28n^2=-96-184n

Solution for 28n^2=-96-184n equation:

Simplifying
28n2 = -96 + -184n

Solving
28n2 = -96 + -184n

Solving for variable 'n'.

Reorder the terms:
96 + 184n + 28n2 = -96 + -184n + 96 + 184n

Reorder the terms:
96 + 184n + 28n2 = -96 + 96 + -184n + 184n

Combine like terms: -96 + 96 = 0
96 + 184n + 28n2 = 0 + -184n + 184n
96 + 184n + 28n2 = -184n + 184n

Combine like terms: -184n + 184n = 0
96 + 184n + 28n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + 46n + 7n2) = 0

Factor a trinomial.
4((6 + n)(4 + 7n)) = 0

Ignore the factor 4.
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 '(4 + 7n)' equal to zero and attempt to solve:

Simplifying
4 + 7n = 0

Solving
4 + 7n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7n = 0 + -4
7n = 0 + -4

Combine like terms: 0 + -4 = -4
7n = -4

Divide each side by '7'.
n = -0.5714285714

Simplifying
n = -0.5714285714
Solution
n = {-6, -0.5714285714}