9a^2+4a+2a+1=0

Solution for 9a^2+4a+2a+1=0 equation:

Simplifying
9a2 + 4a + 2a + 1 = 0

Reorder the terms:
1 + 4a + 2a + 9a2 = 0

Combine like terms: 4a + 2a = 6a
1 + 6a + 9a2 = 0

Solving
1 + 6a + 9a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
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 = {-0.3333333333, -0.3333333333}