6n^2=-288-84n

Solution for 6n^2=-288-84n equation:

Simplifying
6n2 = -288 + -84n

Solving
6n2 = -288 + -84n

Solving for variable 'n'.

Reorder the terms:
288 + 84n + 6n2 = -288 + -84n + 288 + 84n

Reorder the terms:
288 + 84n + 6n2 = -288 + 288 + -84n + 84n

Combine like terms: -288 + 288 = 0
288 + 84n + 6n2 = 0 + -84n + 84n
288 + 84n + 6n2 = -84n + 84n

Combine like terms: -84n + 84n = 0
288 + 84n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(48 + 14n + n2) = 0

Factor a trinomial.
6((8 + n)(6 + n)) = 0

Ignore the factor 6.
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 '(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
Solution
n = {-8, -6}