4n^2+19n+21=0

Solution for 4n^2+19n+21=0 equation:

Simplifying
4n2 + 19n + 21 = 0

Reorder the terms:
21 + 19n + 4n2 = 0

Solving
21 + 19n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(7 + 4n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + 4n)' equal to zero and attempt to solve:

Simplifying
7 + 4n = 0

Solving
7 + 4n = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4n = 0 + -7
4n = 0 + -7

Combine like terms: 0 + -7 = -7
4n = -7

Divide each side by '4'.
n = -1.75

Simplifying
n = -1.75
Solution
n = {-3, -1.75}