6(n^2+2)=-2(19n)

Solution for 6(n^2+2)=-2(19n) equation:

Simplifying
6(n2 + 2) = -2(19n)

Reorder the terms:
6(2 + n2) = -2(19n)
(2 * 6 + n2 * 6) = -2(19n)
(12 + 6n2) = -2(19n)

Remove parenthesis around (19n)
12 + 6n2 = -2 * 19n

Multiply -2 * 19
12 + 6n2 = -38n

Solving
12 + 6n2 = -38n

Solving for variable 'n'.

Reorder the terms:
12 + 38n + 6n2 = -38n + 38n

Combine like terms: -38n + 38n = 0
12 + 38n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 19n + 3n2) = 0

Factor a trinomial.
2((6 + n)(1 + 3n)) = 0

Ignore the factor 2.
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 '(1 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

Solving
1 + 3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3n = 0 + -1
3n = 0 + -1

Combine like terms: 0 + -1 = -1
3n = -1

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {-6, -0.3333333333}