20a^2+41a+9=0

Solution for 20a^2+41a+9=0 equation:

Simplifying
20a2 + 41a + 9 = 0

Reorder the terms:
9 + 41a + 20a2 = 0

Solving
9 + 41a + 20a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9 + 5a)(1 + 4a) = 0

Subproblem 1
Set the factor '(9 + 5a)' equal to zero and attempt to solve:

Simplifying
9 + 5a = 0

Solving
9 + 5a = 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 + 5a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5a = 0 + -9
5a = 0 + -9

Combine like terms: 0 + -9 = -9
5a = -9

Divide each side by '5'.
a = -1.8

Simplifying
a = -1.8
Subproblem 2
Set the factor '(1 + 4a)' equal to zero and attempt to solve:

Simplifying
1 + 4a = 0

Solving
1 + 4a = 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 + 4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4a = 0 + -1
4a = 0 + -1

Combine like terms: 0 + -1 = -1
4a = -1

Divide each side by '4'.
a = -0.25

Simplifying
a = -0.25
Solution
a = {-1.8, -0.25}