3a^2+16a+21=0

Solution for 3a^2+16a+21=0 equation:

Simplifying
3a2 + 16a + 21 = 0

Reorder the terms:
21 + 16a + 3a2 = 0

Solving
21 + 16a + 3a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

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

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(7 + 3a)' equal to zero and attempt to solve:

Simplifying
7 + 3a = 0

Solving
7 + 3a = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3a = 0 + -7
3a = 0 + -7

Combine like terms: 0 + -7 = -7
3a = -7

Divide each side by '3'.
a = -2.333333333

Simplifying
a = -2.333333333
Solution
a = {-3, -2.333333333}