27w^2+9w-6=0

Solution for 27w^2+9w-6=0 equation:

Simplifying
27w2 + 9w + -6 = 0

Reorder the terms:
-6 + 9w + 27w2 = 0

Solving
-6 + 9w + 27w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3w + 9w2) = 0

Factor a trinomial.
3((-2 + -3w)(1 + -3w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -3w)' equal to zero and attempt to solve:

Simplifying
-2 + -3w = 0

Solving
-2 + -3w = 0

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

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

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

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

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

Simplifying
w = -0.6666666667
Subproblem 2
Set the factor '(1 + -3w)' equal to zero and attempt to solve:

Simplifying
1 + -3w = 0

Solving
1 + -3w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3w = 0 + -1

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

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

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

Simplifying
w = 0.3333333333
Solution
w = {-0.6666666667, 0.3333333333}