36n^2+224n+48=0

Solution for 36n^2+224n+48=0 equation:

Simplifying
36n2 + 224n + 48 = 0

Reorder the terms:
48 + 224n + 36n2 = 0

Solving
48 + 224n + 36n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 56n + 9n2) = 0

Factor a trinomial.
4((6 + n)(2 + 9n)) = 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 '(2 + 9n)' equal to zero and attempt to solve:

Simplifying
2 + 9n = 0

Solving
2 + 9n = 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 + 9n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9n = 0 + -2
9n = 0 + -2

Combine like terms: 0 + -2 = -2
9n = -2

Divide each side by '9'.
n = -0.2222222222

Simplifying
n = -0.2222222222
Solution
n = {-6, -0.2222222222}