6a^2+22a=-16

Solution for 6a^2+22a=-16 equation:

Simplifying
6a2 + 22a = -16

Reorder the terms:
22a + 6a2 = -16

Solving
22a + 6a2 = -16

Solving for variable 'a'.

Reorder the terms:
16 + 22a + 6a2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + 22a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 11a + 3a2) = 0

Factor a trinomial.
2((8 + 3a)(1 + a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 3a)' equal to zero and attempt to solve:

Simplifying
8 + 3a = 0

Solving
8 + 3a = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3a = 0 + -8
3a = 0 + -8

Combine like terms: 0 + -8 = -8
3a = -8

Divide each side by '3'.
a = -2.666666667

Simplifying
a = -2.666666667
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Solution
a = {-2.666666667, -1}