7n^2+22n+16=0

Solution for 7n^2+22n+16=0 equation:

Simplifying
7n2 + 22n + 16 = 0

Reorder the terms:
16 + 22n + 7n2 = 0

Solving
16 + 22n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + n)(8 + 7n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + 7n)' equal to zero and attempt to solve:

Simplifying
8 + 7n = 0

Solving
8 + 7n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7n = 0 + -8
7n = 0 + -8

Combine like terms: 0 + -8 = -8
7n = -8

Divide each side by '7'.
n = -1.142857143

Simplifying
n = -1.142857143
Solution
n = {-2, -1.142857143}