3n^2+49n+16=0

Solution for 3n^2+49n+16=0 equation:

Simplifying
3n2 + 49n + 16 = 0

Reorder the terms:
16 + 49n + 3n2 = 0

Solving
16 + 49n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(16 + n)(1 + 3n) = 0

Subproblem 1
Set the factor '(16 + n)' equal to zero and attempt to solve:

Simplifying
16 + n = 0

Solving
16 + n = 0

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

Add '-16' to each side of the equation.
16 + -16 + n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + n = 0 + -16
n = 0 + -16

Combine like terms: 0 + -16 = -16
n = -16

Simplifying
n = -16
Subproblem 2
Set the factor '(1 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

Solving
1 + 3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3n = 0 + -1
3n = 0 + -1

Combine like terms: 0 + -1 = -1
3n = -1

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {-16, -0.3333333333}