27a^2-54a+15=0

Solution for 27a^2-54a+15=0 equation:

Simplifying
27a2 + -54a + 15 = 0

Reorder the terms:
15 + -54a + 27a2 = 0

Solving
15 + -54a + 27a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -18a + 9a2) = 0

Factor a trinomial.
3((1 + -3a)(5 + -3a)) = 0

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

Simplifying
1 + -3a = 0

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

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

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

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
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 = {0.3333333333, 1.666666667}