28n^2=-72-180n

Solution for 28n^2=-72-180n equation:

Simplifying
28n2 = -72 + -180n

Solving
28n2 = -72 + -180n

Solving for variable 'n'.

Reorder the terms:
72 + 180n + 28n2 = -72 + -180n + 72 + 180n

Reorder the terms:
72 + 180n + 28n2 = -72 + 72 + -180n + 180n

Combine like terms: -72 + 72 = 0
72 + 180n + 28n2 = 0 + -180n + 180n
72 + 180n + 28n2 = -180n + 180n

Combine like terms: -180n + 180n = 0
72 + 180n + 28n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + 45n + 7n2) = 0

Factor a trinomial.
4((6 + n)(3 + 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 '(3 + 7n)' equal to zero and attempt to solve:

Simplifying
3 + 7n = 0

Solving
3 + 7n = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7n = 0 + -3
7n = 0 + -3

Combine like terms: 0 + -3 = -3
7n = -3

Divide each side by '7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Solution
n = {-6, -0.4285714286}