6x^2-28x+22=0

Solution for 6x^2-28x+22=0 equation:

Simplifying
6x2 + -28x + 22 = 0

Reorder the terms:
22 + -28x + 6x2 = 0

Solving
22 + -28x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -14x + 3x2) = 0

Factor a trinomial.
2((1 + -1x)(11 + -3x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {1, 3.666666667}