4n^2+52n+120=0

Solution for 4n^2+52n+120=0 equation:

Simplifying
4n2 + 52n + 120 = 0

Reorder the terms:
120 + 52n + 4n2 = 0

Solving
120 + 52n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + 13n + n2) = 0

Factor a trinomial.
4((10 + n)(3 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {-10, -3}