27u^2-12u+1=0

Solution for 27u^2-12u+1=0 equation:

Simplifying
27u2 + -12u + 1 = 0

Reorder the terms:
1 + -12u + 27u2 = 0

Solving
1 + -12u + 27u2 = 0

Solving for variable 'u'.

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

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

Simplifying
1 + -9u = 0

Solving
1 + -9u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -9u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9u = 0 + -1
-9u = 0 + -1

Combine like terms: 0 + -1 = -1
-9u = -1

Divide each side by '-9'.
u = 0.1111111111

Simplifying
u = 0.1111111111
Subproblem 2
Set the factor '(1 + -3u)' equal to zero and attempt to solve:

Simplifying
1 + -3u = 0

Solving
1 + -3u = 0

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

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

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

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

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

Simplifying
u = 0.3333333333
Solution
u = {0.1111111111, 0.3333333333}