21X^2-27X+6=0

Solution for 21X^2-27X+6=0 equation:

Simplifying
21X2 + -27X + 6 = 0

Reorder the terms:
6 + -27X + 21X2 = 0

Solving
6 + -27X + 21X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -9X + 7X2) = 0

Factor a trinomial.
3((2 + -7X)(1 + -1X)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -7X)' equal to zero and attempt to solve:

Simplifying
2 + -7X = 0

Solving
2 + -7X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7X = 0 + -2
-7X = 0 + -2

Combine like terms: 0 + -2 = -2
-7X = -2

Divide each side by '-7'.
X = 0.2857142857

Simplifying
X = 0.2857142857
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 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 + -1X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {0.2857142857, 1}