8a^2-27a+9=0

Solution for 8a^2-27a+9=0 equation:

Simplifying
8a2 + -27a + 9 = 0

Reorder the terms:
9 + -27a + 8a2 = 0

Solving
9 + -27a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -8a)(3 + -1a) = 0

Subproblem 1
Set the factor '(3 + -8a)' equal to zero and attempt to solve:

Simplifying
3 + -8a = 0

Solving
3 + -8a = 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 + -8a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8a = 0 + -3
-8a = 0 + -3

Combine like terms: 0 + -3 = -3
-8a = -3

Divide each side by '-8'.
a = 0.375

Simplifying
a = 0.375
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 = {0.375, 3}