3n^2=-32-28n

Solution for 3n^2=-32-28n equation:

Simplifying
3n2 = -32 + -28n

Solving
3n2 = -32 + -28n

Solving for variable 'n'.

Reorder the terms:
32 + 28n + 3n2 = -32 + -28n + 32 + 28n

Reorder the terms:
32 + 28n + 3n2 = -32 + 32 + -28n + 28n

Combine like terms: -32 + 32 = 0
32 + 28n + 3n2 = 0 + -28n + 28n
32 + 28n + 3n2 = -28n + 28n

Combine like terms: -28n + 28n = 0
32 + 28n + 3n2 = 0

Factor a trinomial.
(8 + n)(4 + 3n) = 0

Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 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 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Solution
n = {-8, -1.333333333}