27a^2-6a-8=0

Solution for 27a^2-6a-8=0 equation:

Simplifying
27a2 + -6a + -8 = 0

Reorder the terms:
-8 + -6a + 27a2 = 0

Solving
-8 + -6a + 27a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4 + -9a)(2 + -3a) = 0

Subproblem 1
Set the factor '(-4 + -9a)' equal to zero and attempt to solve:

Simplifying
-4 + -9a = 0

Solving
-4 + -9a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9a = 0 + 4
-9a = 0 + 4

Combine like terms: 0 + 4 = 4
-9a = 4

Divide each side by '-9'.
a = -0.4444444444

Simplifying
a = -0.4444444444
Subproblem 2
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {-0.4444444444, 0.6666666667}