19a^2-66a+27=0

Solution for 19a^2-66a+27=0 equation:

Simplifying
19a2 + -66a + 27 = 0

Reorder the terms:
27 + -66a + 19a2 = 0

Solving
27 + -66a + 19a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9 + -19a)(3 + -1a) = 0

Subproblem 1
Set the factor '(9 + -19a)' equal to zero and attempt to solve:

Simplifying
9 + -19a = 0

Solving
9 + -19a = 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 + -19a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -19a = 0 + -9
-19a = 0 + -9

Combine like terms: 0 + -9 = -9
-19a = -9

Divide each side by '-19'.
a = 0.4736842105

Simplifying
a = 0.4736842105
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {0.4736842105, 3}