27x^2-51x+14=0

Solution for 27x^2-51x+14=0 equation:

Simplifying
27x2 + -51x + 14 = 0

Reorder the terms:
14 + -51x + 27x2 = 0

Solving
14 + -51x + 27x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -3x)(14 + -9x) = 0

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

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

Simplifying
x = 0.3333333333
Subproblem 2
Set the factor '(14 + -9x)' equal to zero and attempt to solve:

Simplifying
14 + -9x = 0

Solving
14 + -9x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -9x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -9x = 0 + -14
-9x = 0 + -14

Combine like terms: 0 + -14 = -14
-9x = -14

Divide each side by '-9'.
x = 1.555555556

Simplifying
x = 1.555555556
Solution
x = {0.3333333333, 1.555555556}