2n^2+28n+48=0

Solution for 2n^2+28n+48=0 equation:

Simplifying
2n2 + 28n + 48 = 0

Reorder the terms:
48 + 28n + 2n2 = 0

Solving
48 + 28n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 14n + n2) = 0

Factor a trinomial.
2((12 + n)(2 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-12, -2}