4n^2+34n+72=0

Solution for 4n^2+34n+72=0 equation:

Simplifying
4n2 + 34n + 72 = 0

Reorder the terms:
72 + 34n + 4n2 = 0

Solving
72 + 34n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 17n + 2n2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + 2n)' equal to zero and attempt to solve:

Simplifying
9 + 2n = 0

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

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

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

Divide each side by '2'.
n = -4.5

Simplifying
n = -4.5
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-4.5, -4}