18a^2+138a+180=0

Solution for 18a^2+138a+180=0 equation:

Simplifying
18a2 + 138a + 180 = 0

Reorder the terms:
180 + 138a + 18a2 = 0

Solving
180 + 138a + 18a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(30 + 23a + 3a2) = 0

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

Ignore the factor 6.
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 '(5 + 3a)' equal to zero and attempt to solve:

Simplifying
5 + 3a = 0

Solving
5 + 3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3a = 0 + -5

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

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

Divide each side by '3'.
a = -1.666666667

Simplifying
a = -1.666666667
Solution
a = {-6, -1.666666667}