5a^2+33a+18=0

Solution for 5a^2+33a+18=0 equation:

Simplifying
5a2 + 33a + 18 = 0

Reorder the terms:
18 + 33a + 5a2 = 0

Solving
18 + 33a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(3 + 5a) = 0

Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 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 + 5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5a = 0 + -3
5a = 0 + -3

Combine like terms: 0 + -3 = -3
5a = -3

Divide each side by '5'.
a = -0.6

Simplifying
a = -0.6
Solution
a = {-6, -0.6}