4n^2+44n+72=0

Solution for 4n^2+44n+72=0 equation:

Simplifying
4n2 + 44n + 72 = 0

Reorder the terms:
72 + 44n + 4n2 = 0

Solving
72 + 44n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + 11n + n2) = 0

Factor a trinomial.
4((9 + n)(2 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

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

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

Simplifying
n = -9
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 = {-9, -2}