6a^2+29a+9=0

Solution for 6a^2+29a+9=0 equation:

Simplifying
6a2 + 29a + 9 = 0

Reorder the terms:
9 + 29a + 6a2 = 0

Solving
9 + 29a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9 + 2a)(1 + 3a) = 0

Subproblem 1
Set the factor '(9 + 2a)' equal to zero and attempt to solve:

Simplifying
9 + 2a = 0

Solving
9 + 2a = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2a = 0 + -9
2a = 0 + -9

Combine like terms: 0 + -9 = -9
2a = -9

Divide each side by '2'.
a = -4.5

Simplifying
a = -4.5
Subproblem 2
Set the factor '(1 + 3a)' equal to zero and attempt to solve:

Simplifying
1 + 3a = 0

Solving
1 + 3a = 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 + 3a = 0 + -1

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

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

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

Simplifying
a = -0.3333333333
Solution
a = {-4.5, -0.3333333333}